Procrastination is hazardous! John Chinchen, LCB 326, ,

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1 Tom Robbins MATH 00- Summer 00 Homework Set due 6/3/0 at 7:00 PM This is the first of WeBWorK based home work sets. Each problem is worth point. These problems are designed to be mathematically easy and only serve to familiarize you with the oddities of WeBWork. In order to receive credit you need to enter correct answers by 7:00 pm on Monday, May 7. You should be able to answer most of these questions right away. Here are some hints on how to use WeBWorK effectively: After first logging into WeBWorK, change your password and set your address. Find out how to print a hard copy on the computer system that you are going to use. Contact me if you have any problems. Print a hard copy of this assignment. Find a place and time when you can work on these problems away from the computer for a sustained period without distractions. Work the problems and record your answers. If you get stuck on one problem, set it aside and later read the relevant section in the textbook, talk to friends, go to the tutoring lab, or send me to find out why you are stuck. Then finish the problem. When you have the answers to the problems go to a computer and enter them. If the system tells you that your answer is wrong try to figure out what happened and reenter the answer. Maybe you mistyped something. If it isn t clear what s wrong answer the remaining questions. Regarding those questions that you could not answer correctly go back to step. Get to work on this set right away and answer these questions well before the deadline. Not only will this give you the chance to figure out what s wrong if an answer is not accepted, you also will avoid the likely rush and congestion prior to the deadline. The primary purpose of the WeBWorK assignments in this class is to give you the opportunity to learn by having instant feedback on your active solution of relevant problems. Make the best of it! Procrastination is hazardous! John Chinchen, LCB 36, , chinchen@math.utah.edu..( pt) This first question is just an exercise in entering numbers into WeBWorK. Of course, you can do this easily, but this problem, your first encounter with a WeBWorK question, shows you what s involved. Notice the buttons on this page and try them out before moving to the next problem. Use the Back Button on your browser to get back here when needed. Prob. List gets you back to the list of all problems in this set. Next gets you to the next question in this set. Submit Answer submits your answer (duh!), but there may be other ways to do so. Specifically, in this problem, there is only one question. In that case you can submit your answer by typing it into the answer window and then pressing Return (or Enter ) on your keyboard. But even in this case, you can also type the answer and click on the submit button. There is no harm in submitting an answer even if you are not quite sure that it s correct, since if it is not you have an united number of additional tries. On the other hand, it is more efficient to print your own private problems set, work out the answers in a quiet environment like your home, and then sit down in front of a computer and enter your answers. If some are wrong you can try to fix them right at the computer, or you may want to go back and work on them quietly elsewhere before returning to the computer. Pressing on the Preview Answer Button makes WeBWorK display what it thinks you entered in the answer window. This will

2 become useful when the answers are more complicated. To become familiar with WeB- WorK, enter something in the answer window below, and press Preview. Try this with fractions like 3/4 and algebraic expressions like (a+b)/(+c). Try it now! (Never mind that these are the wrong answers, and you may have already received credit for typing 3 correctly). typeset denotes the ordinary display mode on your workstation, but formatted text is a little faster, and it may work in some cases when typeset does not. Logout terminates this WeBWorK session for you. You can of course log back in and continue. Feedback enables you to send a message to your instructor (John Chinchen), and the WeBWorK assistants. If you use this way of sending the recipients receive information about your WeBWorK state, in addition to your actual message. The Help Button transports you to an official WeBWorK help page that has a more information than this first problem. Problem Sets transports you back to the page where you can select a certain problem set. When you do this particular problem in this first set, there is only one set, but eventually there will be of them. Now for the meat of this problem. Notice that the answer window is extra large so you can try the things suggested above. Type the number 3 here:..( pt) Wasn t that last problem easy? Here s another easy one. Its purpose is to illustrate further the use of the buttons on this page and to show you the most common way in which WeBWorK processes partially correct problems. Try entering incorrect answers in the answer fields below, to see what happens. Type the number 4 here:. Type the number 5 here:. 3.( pt) We start simply. In the first few problems you will be asked to evaluate some arithmetic expressions and enter the answer as a number into WeB- WorK. You may of course use a calculator. The purpose of these first few problems is to help you get familiar with WeBWorK. In later problems you will be able to enter the answer as an arithmetic expression, but at present your answer must be a number such as 4, -4, or =. 4.( pt) 9 =. 5.( pt) 6 =. (Enter you answer as a decimal number.) 6.( pt) 5 4 =. 7.( pt) 4 7 =..( pt) The next few questions are about fractions. You ll be asked to compute a fraction and reduce it to lowest terms. Note that since there are two parts to the answer you will need to press the submit button below to have your answer evaluated. The expression 3 is a fraction a b where b is positive, and a and b have no common factors. Enter a= and b= 9.( pt) The expression 3 is a fraction a b where b is positive, and a and b have no common factors. Enter a= and b= 0.( pt) The expression is a fraction a b where b is positive, and a and b have no common factors. Enter a= and b=.( pt) 7 is a fraction a b where b is pos- The expression itive, and a and b have no common factors. Enter a= and b=

3 .( pt) The expression is a fraction a b where b is positive, and a and b have no common factors. Enter a= and b= 3.( pt) The expression is a fraction b a where b is positive, and a and b have no common factors. 5 7 Enter a= and b= 4.( pt) = = = 5.( pt) = = = = 6.( pt) Match the statements defined below with the letters labeling their equivalent expressions. You must get all of the answers correct to receive credit.. The distance from x to -6 is more than 3. x is less than x is any real number 4. x is greater than The distance from x to -6 is less than or equal to 3 A. x B. x 6 3 C. 6 x D. x 6 3 E. x 6 7.( pt) Match the statements defined below with the letters labeling their equivalent intervals. You must get all of the answers correct to receive credit.. x 3. x 6 3. x 4. x 5. x 6 A. x 6 B. x 6 C. x D. x E. x.( pt) ( pt) ( pt) ( pt) Give you answer in decimal notation correct to three decimal places or give your answer as a fraction. [NOTE: Your answer can be an algebraic expression. Make sure to include all necessary (, ). ].( pt) Find the distance between 339 and 5. [NOTE: Your answer can be an algebraic expression] 3.( pt) (Your answer cannot be an algebraic expression. ) 4.( pt) Enter a T or an F in each answer space below to indicate whether the corresponding statement is true or false. You must get all of the answers correct to receive credit.. π ( pt) Match the statements defined below with the letters labeling their equivalent expressions. You must get all of the answers correct to receive credit.. x 0. x 0 3. x 0

4 4. x 5. x 0 A. x B. x C. x D. x E. x! Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c UR 4

5 Tom Robbins MATH 00-3 Summer 00 Homework Set due 6/3/0 at 7:00 PM Here is Promblem set. Just a brief review of Math090, and chapter 9.. Have Fun! A reminder for entering your answers: use extra decimals to make sure it will accept your result, and DNE means DNE, not dne. John Chinchen; Office: LCB 36; Phone:55-646, chinchen@math.utah.edu..( pt) The expression 5t 7 equals At Bt C where A equals: and B equals: and C equals: 6t 3 5t 5.( pt) Factor the polynomial x 6x 5. Your answer can be written as x A x B where A B and A equals: and B equals: 3.( pt) Match the expressions below with the letters labeling their equivalent expressions. You must get all of the answers correct to receive credit.. x 7x 6 x x 3 x. x 63 x 5x 54 x 3. 9x x 4x 3 A. x 6 x 3 B. x 6 x C. x 7 x 6 4.( pt) Enter a T or an F in each answer space below to indicate whether the corresponding equation is true or false. An equation is true ony if it is true for all values of the variables. Disregard values that make denominators 0. You must get all of the answers correct to receive credit.. 63 x " x. x y " 3. x y " x y x y a " a 5.( pt) Suppose a mining company will supply 9000 tons of ore per month if the price is 00 dollars per ton but will supply tons per month if the price is 5 dollars per ton. Assuming the supply function is of the form y " mx b, find the slope, m and y-intercept, b m : b: 6.( pt) Let C be the cost function, C x " x x (in blue) and let R be the revenue function, R x " 500x x (in red) below. If you are having a hard time seeing the picture clearly, click on the picture. It will expand to a larger picture on its own page so that you can inspect it more closely. What are the equilibrium points where x x :. x =. x = 7.( pt) Evaluate the following expressions. (a) lne 7 " (b) e ln7 " (c) e ln# 4 " (d) ln e 3 ".( pt) If 3000 dollars is invested in a bank account at an interest rate of percent per year, Find the amount in the bank after 3 years if interest is compounded continuously: How long will it take for 3000 dollars to increase by a factor of two if interest is compounded continuously?

6 9.( pt) Evaluate the it x x 0 x$ 0 x 0 0.( pt) Evaluate the it x 3 x x$ x.( pt) Let f x " 5 if x 0, f x " 5 if x " 0, f x " x 4 if 3 x 0, f x " 7 if x % 3. Sketch the graph of this function and find following its if they exist (if not, enter DNE).. f x x$ 0&. x$ 0' f x 3. x$ f x 0 4. f x x$ 3& 5. f x x$ 3' 6. x$ f x 3! Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c UR

7 - Tom Robbins MATH 00-3 Summer 00 Homework Set 3 due 6/0/0 at 7:00 PM Here is Problem set 3. If you do not understand something, look in chapter 9 of your book. Remember, the tutoring lab is available for your use free of charge. Good luck! John Chinchen; Office: LCB 36; Phone:55-646, chinchen@math.utah.edu..( pt) The slope of the tangent line to the graph of the function y " x 3 at the point 3 54 is x($ x x 3. By trying values of x near 3, find the slope of the tangent line. I would suggest picking a value so near 3 that you are only under or over. This will give you a more accurate representation of what is occuring near the point..( pt) Evaluate the it x x$ x 9x 0 9. x$ a h x * f x 5.( pt) Let F be the function below. If you are having a hard time seeing the picture clearly, click on the picture. It will expand to a larger picture on its own page so that you can inspect it more clearly. 3.( pt) Let f x " x 5 if x and f x " 5 if x. Sketch the graph of this function for yourself and find following its if they exist (if not, enter N).. f x x$ &. f x x$ ' 3. x$ f x 4.( pt) Let g x x$ a ", h x x$ a ", x$ f x a " 0. Find following its if they exist. If not, enter DNE ( does not exist ) as your answer.. g x ) h x x$ a. g x * h x x$ a 3. g x,+ f x x$ a g x 4. x$ a h x g x 5. x$ a f x f x 6. x$ a g x 7. h x x$ a. h x x$ a Evaluate each of the following expressions. Note: Enter DNE if the it does not exist or is not defined. a) F x = x$ & b) F x = x$ ' c) x$ F x = d) F = e) F x = x$ & f) F x = x$ ' g) x$ F x = h) x$ F x = 3 i) F 3 = 6.( pt) Evaluate the it 5 9x x$ 6x

8 7.( pt) Evaluate the it x 3 x$ 3x 5x 7.( pt) Evaluate the it 5x 3 x 5x x$ 9 0x 0x 3 9.( pt) Evaluate the it x$ 0 x 6x 3 6x 6 6x 0.( pt) If f x " 3, find f..( pt) If f x " 4x, find f. Find f. 5.. x..( pt) If f x " 5x 5x 37, find f. Find f.. 3.( pt) If f t " 4t 3, find f. Find f.. 4.( pt) If f t ", find f. t. t 4 t. x. [NOTE: Your answer should be a function in terms of the variable t and not a number! ] 5.( pt) If f 7 x " 5 x, find f. x. x 6.( pt) If f x " x 5, find f ( pt) If f x " 7 4x 4x, find f. 0..( pt) If f x " 9.( pt) Let 4, find f.. x f x "0/ x f. 3 " 0.( pt) If f x " 6x 3x, find f. first distributing using the FOIL method..( pt) If f x " 6x 4 using the PRODUCT RULE. 6x, find f. x by x by.( pt) Let f 4 x " 7x 3. Use the QUOTIENT RULE to find f. x " 3.( pt) If f 4 x x " 4 x find f. x using the QUOTIENT RULE. Find f.. 4.( pt) For the given cost function C x " x x find: a) The cost at the production level 00 b) The marginal cost at the production level 00 5.( pt) For the given cost function C x " x 4x and the demand fuction p x " 430. Find the production level that will maximize profit. Remember, the Profit function is the difference between the Revenue and the Cost functions. Also, you can find the Revenue function by multiplying the demand function p x " 430 by x. One more reminder, the Profit function will be maximized when the derivative is zero.! Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c UR

9 Tom Robbins MATH 00- Summer 00 Homework Set 4 due 6/7/0 at 7:00 PM Here is Problem set 4. If you do not understand something, check the book for additional examples. Remember, the tutoring lab is available for your use free of charge. Good luck! John Chinchen; Office: LCB 36; Phone:55-646, chinchen@math.utah.edu..( pt) Evaluate the it x 4x 4 x$ 6 x 6.( pt) Evaluate the it 5x 3 0x 0x x$ 9 x x 3 3.( pt) Evaluate the it x$ 3 x 9 5x 3 6x 9 5x 4.( pt) If the tangent line to y " f x at (3, -) passes through the point (-3, -6), find A. f 3 " B. f. 3 " 5.( pt) The area of a square with side s is A s " s. What is the rate of change of the area of a square with respect to its side length when s " 7? 6.( pt) The population of a slowly growing bacterial colony after t hours is given by p t " 5t 3t 00. Find the growth rate after 4 hours. 7.( pt) The cost of producing x units of stuffed alligator toys is c x " 0 004x 0x Find the marginal cost at the production level of 000 units..( pt) A particle moves along a straight line with equation of motion s " t 6 t 5 Find the value of t (other than 0 ) at which the acceleration is equal to zero. 9.( pt) Let f. f. x " 4 " f x " 0.( pt) If f x " x 3 4x 4 5x 5 6x 4 7x 3, find f. x. x 4.( pt) If f x " 5x 03 x 3, find f. x..( pt) Let h x " 4x x 4. Then h. x is and h.4. x is 3.( pt) Let f x " 5x 5. Then f. x is and f.4. x is 4.( pt) Let f x " / 3x 3. Then f. x is and f.4. x is 5.( pt) Let f. x " f. 4 " 6.( pt) Let f. x " f. e 3 " 7.( pt) Let f x " ln 6x f x " ln x 6 f x " lnx 7 f. x " f. e 4 ".( pt) Use the change of base formula to find the derivative of f x " log 9 x f. x " f. " 9.( pt) Let f x " 7e x e. f. 0 " 0.( pt) Find the derivative of the function g x " 4x 5x 0 e x g. x ".( pt) Find the derivative of the function g e x x " 5 x

10 g. x ".( pt) Use implicit differentiation to find the slope of the tangent line to the curve 4x y " 0 at the point. m "! Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c UR

11 Tom Robbins MATH 00-3 Summer 00 Homework Set 5 due 6/4/0 at 7:00 PM Here is Problem Set 5. This should be a decent review for your test on Friday. If you do not understand something, check the book for additional examples. Remember, the tutoring lab is available for your use free of charge. Good luck! John Chinchen; Office: LCB 36; Phone:55-646, chinchen@math.utah.edu. 5.( pt) If f x " 3 / xln x, find f. Find f...( pt) Let f x " 3x 6 lnx f. x " f. e 4 " 3.( pt) Let F be the function below. If you are having a hard time seeing the picture clearly, click on the picture. It will expand to a larger picture on its own page so that you can inspect it more clearly. Evaluate each of the following expressions. Note: Enter DNE if the it does not exist or is not defined. a) F x = x$ & b) F x = x$ ' c) x$ F x = d) F = e) F x = x$ & x. f) F x = x$ ' g) x$ F x = h) x$ F x = 3 i) F 3 = 4.( pt) Let f x 6 x log 4 x f x 5.( pt) Evaluate the following its. If needed, enter INF for and MINF for. (a) 3x 4 x$ 3x 3x 4 (b) 6.( pt) Let f. x " 7.( pt) If f x " 3x 4 x$ 3x 3x 4 f x " ln x 3x 7x 6x, find f #. 4. x.( pt) Let f x " 4e x e. f. 0 " [NOTE: A small algebraic manipulation is needed first to get f(x) into a form so that the derivative can be taken.] 9.( pt) Find the derivative of the function g x " 5x x e x g. x " 0.( pt) Find the derivative of the function g e x x " 3x

12 g. x ".( pt) If f x " / 0x, find f. x..( pt) Find the slope of the tangent line to the curve 3x 4xy y 3 " 3 at the point. 3.( pt) Use implicit differentiation to find the slope of the tangent line to the curve at the point. m " x xy 4y 3 " 4! Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c UR

13 Tom Robbins MATH 00-3 Summer 00 Homework Set 6 due 7//0 at 7:00 PM Here is Problem set 6. If you do not understand something, check the book for additional examples. Remember, the tutoring lab is available for your use free of charge. Good luck! For reference, refer to chapter 0.. John Chinchen; Office: LCB 36; Phone:55-646, chinchen@math.utah.edu. -.( pt) Use implicit differentiation to find the slope of the tangent line to the curve 3x 4xy 3y 3 " 44 at the point 3 3. m ".( pt) Use implicit differentiation to find the slope of the tangent line to the curve y x 4y " x 3 at the point 7. m " 3.( pt) The function f x " x 3 x 36x has two critical values. The smaller one equals and the larger one equals 4.( pt) The function f x " x 3 x 7x 9 has one relative minimum and one relative maximum. This function has a relative minimum at x equals with value and a relative maximum at x equals with value 5.( pt) The function f x " x 3 30x 6x has one relative minimum and one relative maximum. This function has a relative minimum at x equals with value and a relative maximum at x equals with value 6.( pt) The function f x " x 4x has one relative minimum and one relative maximum. This function has a relative minimum at x equals with value and a relative maximum at x equals with value 7.( pt) For x 6 5 the function f is defined by f x " x 7 x 5 On which two intervals is the function increasing (enter intervals in ascending order)? to and to Find the region in which the function is positive: to Where does the function achieve its minimum?.( pt) Consider the function f x " 6x x. For this function there are four important intervals: A, A B, B C, and C where A, and C are the critical numbers and the function is not defined at B. Find A and B and C For each of the following intervals, tell whether f x is increasing (type in INC) or decreasing (type in DEC). A : A B : B C : C : 9.( pt) Answer the following questions for the function f x " x x 5 defined on the interval A. f x is concave down on the region to B. f x is concave up on the region to C. The inflection point for this function is at D. The minimum for this function occurs at E. The maximum for this function occurs at 0.( pt) Consider the function f e x x " 5 e x Then f. x = The following questions ask for endpoints of intervals of increase or decrease for the function f x.

14 Write INF for, MINF for, and NA (ie. not applicable) if there are no intervals of that type. The interval of increase for f x is from to The interval of decrease for f x is from to f x has a local minimum at. (Put NA if none.) f x has a local maximum at. (Put NA if none.) Then f.4. x = The following questions ask for endpoints of intervals of upward and downward concavity for the function f x. Write INF for, MINF for, and put NA if there are no intervals of that type. The interval of upward concavity for f x is from to The interval of downward concavity for f x is from to f x has a point of inflection at. (Put NA if none.)! Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c UR

15 Tom Robbins MATH 00-3 Summer 00 Homework Set 7 due 7//0 at 7:00 PM Here is Problem set 7. If you do not understand something, check the book for additional examples. Remember, the tutoring lab is available for your use free of charge. Good luck! John Chinchen; Office: LCB 36; Phone:55-646, chinchen@math.utah.edu..( pt) The function f x " 4x 3 6x 360x 4 " is decreasing on the interval (, ). It is increasing on the interval (, ) and the interval (, ). The function has a local maximum at..( pt) The function f x 3x 4x has one local minimum and one local maximum. This function has a local minimum at x equals with value and a local maximum at x equals with value 3.( pt) Consider the function f x " 6x 6x. f x is increasing on the interval A and decreasing on the interval A where A is the critical number. Find A At x " A, does f x have a local min, a local max, or neither? You should be aware that there are two different tests that may work. Either use the Second Derivative test and look at concavity at A, or use the First Derivative test and examine the sign table. Type in your answer as LMIN, LMAX, or NEITHER. 4.( pt) Consider the function f x " x4 6 6 x 3 5 x 9x 4. f x has two inflection points (keep in mind that the Second Derviative is real handy in determining these!) at x = C and x = D with C D where C is and D is Finally for each of the following intervals, tell whether f x is concave up (type in CU) or concave down (type in CD). C : C D : D 5.( pt) For the given cost function C x " x x find: a) The cost at the production level 50 b) The average cost at the production level 50 c) The marginal cost at the production level 50 d) The production level that will minimize the average cost e) The minimal average cost 6.( pt) For the given cost function C x " x / x 3375 find a) The cost at the production level 000 b) The average cost at the production level 000 c) The marginal cost at the production level 000 d) The production level that will minimize the average cost. e) The minimal average cost. 7.( pt) A rancher wants to fence in an area of,000,000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?.( pt) You have determined that your business (selling birdhouses) generally follows the given cost function: C x " x 0 5x with the demand fuction p x " 750. Find the monthly production level that will maximize your profit. 9.( pt) The manager of a large apartment complex knows from experience that 0 units will be occupied if the rent is 340 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 0 dollar increase in rent. Similarly, one additional unit will be occupied for each 0 dollar decrease in rent. What rent should the manager charge to maximize revenue? Hint: an example similar to this is given on page 767 in your text. 0.( pt) Consider the function f x " x 3 5x 0x 9.

16 An antiderivative of f x is F x " Ax 4 Bx 3 Cx Dx where A is and B is and C is and D is.( pt) Consider the function f x " 6x 3 x 6x 0. Enter an antiderivative of f x.( pt) Consider the function f x " 5x 9 9x 6 5x 4 7. Enter an antiderivative of f x " " 3.( pt) Consider the function f x 0x 0 x 7 6x. An antiderivative of f x is F x Ax n Bx m Cx p Dx q where A is and n is and B is and m is and C is and p is and D is and q is! Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c UR

17 Tom Robbins MATH 00- Summer 00 Homework Set due 7/5/0 at 7:00 PM Here is Problem set. This might seem like a longer assignment, but many of the problems involve integration, and u substitutions of various types. Once you get good at them, they should go relatively quickly. Set is primarily recent material, with a few reminder problems at the end giving you an idea of what might show up on Monday - Test Day. John Chinchen; Office: LCB 36; Phone:55-646, chinchen@math.utah.edu x x 7.( pt) Consider the function f x " Let F x be the antiderivative of f x with F " 0. Hint: F()=0 just gives us that coordinate point we need to determine the constant, C. Then F x " 0 4 x.( pt) Consider the function f x ". x 7 Let F x be the antiderivative of f x with F " 0. Then F equals 3.( pt) Note: You can get full credit for this problem by just answering the last question correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit. Consider the indefinite integral x x 7: dx Then the most appropriate substitution to simplify this integral is u = Then dx " f x du where f x = After making the substitution we obtain the integral g u du where g u = This last integral is: = C (Leave out constant of integration from your answer.) After substituting back for u we obtain the following final form of the answer: = C (Leave out constant of integration from your answer.) 4.( pt) Evaluate the integral by making the given substitution. dx 3x 4 3 u " 3x 4 5.( pt) Find F x " x x 3 dx Give a specific function for F x. F(x) = 6.( pt) 3 / e x dx = + C 7.( pt) Evaluate the indefinite integral. x e x3 dx.( pt) Evaluate the indefinite integral. x 3-6 x 4 dx 9.( pt) Evaluate the indefinite integral. 5 t 3 dt 0.( pt) Evaluate the indefinite integral. x 3 x 4 5 dx.( pt) Evaluate the indefinite integral. x x 4x dx.( pt) Evaluate the indefinite integral. x 3 x 6x 0 dx 3.( pt) Evaluate the indefinite integral. 4x 4x x 3 3 dx 4.( pt) Coffee is poured into one of mugs above at a constant rate (constant volume per unit time). The graph

18 below shows the depth of coffee in the mug as a function of time. (Click on images for better view.) Which mug was filled with coffee? For credit on this problem, send me a feedback EXPLAINING your choice. This problem is fun, but too easy to just guess away at. Enjoy your Java!! And yes, I will keep track of who sends the feedback! 5.( pt) Consider the function f x " 4 x 3 x. The absolute maximum value is and this occurs at x equals The absolute minimum value is and this occurs at x equals 6.( pt) For x 7 3 the function f is defined by f x " x 4 x 7 7 On which two intervals is the function increasing? to and to Find the region in which the function is positive: to Where does the function achieve its minimum? 7.( pt) Use implicit differentiation to find the slope of the tangent line to the curve at the point 9. m " xy 3 xy "! Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c UR

19 Tom Robbins MATH 00- Summer 00 Homework Set 9 due 7/9/0 at 7:00 PM Here is Problem Set 9. Note that there are ten problems valued at points each, so this set is worth 0 points total. Have Fun :) John Chinchen; Office: LCB 36; Phone:55-646, chinchen@math.utah.edu. -.( pts) Given f.;. x " 4x and f. 3 " 5 and f 3 " 3. Hint: start with integrating the second derivative function, and use the fixed point f. 3 " 5. Then solve for C, giving you the first derivative function. Now integrate this function, and use the second fixed point given to solve the second part of the problem. Find f. x " and find f ".( pts) A particle is moving with acceleration a t " t. its position at time t " 0 is s 0 " 3 and its velocity at time t " 0 is v 0 " 3. Hint: this is the same problem as the first. Treat acceleration as the second derivative and velocity as the first derivative, with the distance being the original function. What is its position at time t " 9? 3.( pts) A car traveling at 45 ft/sec begins decelerating (time is zero here, as is position) at a constant 5 feet per second squared. How many feet does the car travel before coming to a complete stop? Yet another hint: is the acceleration positive or negative? Then, determine the velocity function by integrating the acceleration function, and solving for C (the fixed point will be the velocity of the car at t=0). Integrate the velocity function to determine the position function, and solve for C (the fixed point will be the position when t=0 - and I gave that info above). One more thing...to find how long it will take to stop (which you will need in order to determine how many feet it takes to stop) you will need to use the velocity function and solve for t when v(t)=0. whew!! Maybe not so easy?!? 4.( pts) A ball is shot straight up into the air with initial velocity of 46 ft/sec. Assuming that the air resistance can be ignored, how high does it go? Hint four million and fifty-eight: now this one is identical to the previous, except for now we don t have a car decelerating on the horizontal, we have a ball decelerating in the vertical. Again, the acceleration is constant-is it positive or negative? ps: if any of you ever take a basic course in physics, you will encounter approximately a billion of these types of problems. Hint: The acceleration due to gravity is 3 ft per second squared. 5.( pts) Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using your knowledge of (hint again) circles ( pts) The value of 49 x dx 4 5 dx is x 7.( pts) Evaluate the definite integral 7 x 6 dx.( pts) Evaluate the definite integral 3 x x dx 9.( pts) Evaluate the definite integral x dx 0.( pts) The velocity function is v t " t 3t for a particle moving along a line. Find the displacement (net distance covered) of the particle during the time interval [-,5]. displacement =! Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c UR

20 Tom Robbins MATH 00- Summer 00 Homework Set 0 due /5/0 at 7:00 PM Here is Problem Set 0. Note that there are ten problems valued at points each, so this set is worth 0 points total. Have Fun :) John Chinchen; Office: LCB 36; Phone:55-646, chinchen@math.utah.edu..( pts) Evaluate the indefinite integral. ln x 4 dx x Hint: you should let u=ln(x), and go from there. You may need this same hint later on in the set, so keep it in mind. C.( pts) Evaluate the definite integral. 4 dx x ( pts) Sketch the region enclosed by the given curves. Don t forget to find the points of intersection, they are important in setting up your integral. Then find the area of the region. y " 3x y " 7x 4.( pts) Sketch the region enclosed by the given curves. Then find the area of the region. y " e 5x y " e x x " 5.( pts) Sketch the region enclosed by the given curves. Then find the area of the region. y " 4x y " x 6 Find the area enclosed between f x " 0 6x and g x " x From x " to x " 6 7.( pts) Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep safe. Since Dr. Jones is a mathematician, she suggests building fences described by y " x and y " x 0. Farmer Jones thinks this would be much harder than just building an enclosure with straight sides, but he wants to please his wife. What is the area of the enclosed region?.( pts) Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as divergent. 0 6e x dx 9.( pts) Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as divergent. x 3 3< dx 0.( pts) Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as divergent. 6.( pts) ln x x dx

21 ! Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c UR