WeBWorK demonstration assignment

Transcription

1 WeBWorK demonstration assignment The main purpose of this WeBWorK set is to familiarize yourself with WeBWorK Here are some hints on how to use WeBWorK effectively: After first logging into WeBWorK change your password Find out how to print a hard copy on the computer system that you are going to use Print a hard copy of this assignment 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! ( pt) setdemo/demo prpg Evaluate 9 7 = ( pt) setdemo/demo prpg Evaluate 8 9 = Enter you answer as a decimal number listing at least decimal digits (WeBWorK will reject your answer if it differs by more than one tenth of percent from what it thinks the answer is) 3( pt) setdemo/demo pr3pg Let r 5 Evaluate π r Net, enter π r and let WeBWorK compute the result ( pt) setdemo/demo prpg a b a b 5( pt) setdemo/demo pr5pg a b a b c d If WeBWorK rejects your answer use the preview button to see what it thinks you are trying to tell it 6( pt) setdemo/demo pr6pg a b a a b a b a b 7( pt) setdemo/demo pr7pg y y y y 8( pt) setdemo/demo pr8pg b b ac a Note: this is an epression that gives the solution of a quadratic equation by the quadratic formula

2 Shawn Harrison WW Prob Lib Math -, Fall 3 WeBWorK assignment due 9/5/3 at :59 PM ( pt) set/srw 3 7-pg Evaluate the following epressions (a) log 6 6 (b) log 3 7 (c) log (d) log ( pt) set/srw pg Evaluate the following epressions (a) lne 3 (b) e ln (c) e ln 3 (d) ln e 5 3( pt) set/srw 3 8pg If ln 7 5 3, then ( pt) set/srw 3 5pg If e 7, then 5( pt) set/srw 9pg is equal to ln r 5 s 5 r 5 s 3 Alnr Blns where A and where B 6( pt) set/mecpg has two solutions The smaller one is: and the larger one is: The equation e 5e 6 7( pt) set/ur log pg Determine the smallest integer that satisfies the given inequality ( pt) set/golden-mathspring--q8pg Let f ln cos Assume that is restricted so that ln is defined Find f π 9( pt) set/golden-mathspring--q9pg Find the integral t t t 3 dt ( pt) set/golden-mathspring--qpg The rate of transmission in a telegraph cable is observed to be proportional to ln, where is the ratio of the radius of the core to the thickness of the insulation ( ) What value of gives the maimum rate of transmission? ( pt) set/golden-mathspring--qpg Suppose y 3 Find dy by logarithmic differentiation See Eample 7 in Section 7 of your tet ( pt) set/golden-mathspring--qpg Evaluate π 3 tan 3( pt) set/golden-mathspring--q6pg Find the integral e e C ( pt) set/golden-mathspring--q7pg Find the integral e 3

3 5( pt) set/golden-mathspring--q9pg ln ln for in Find Let f a) lim f b) lim f 6( pt) set/golden-mathspring--qpg The loudness of sound is measured in decibels in honor of Aleander Graham Bell (87-9), inventor of the telephone If the variation in pressure is P pounds per square inch, then the loudness L in decibels is L log 3P Find the variation in pressure caused by a rock band at 5 decibels pounds per square inch

4 Shawn Harrison WW Prob Lib Math -, Fall 3 WeBWorK assignment due 9/6/3 at 6: PM ( pt) set/ur le pg A certain bacteria population is known to quadruple every 9 minutes Suppose that there are initially 3 bacteria What is the size of the population after t hours? ( pt) set/srw 5 8pg If a bacteria culture starts with bateria and doubles every minutes, how many minutes will it take the population to reach 6? 3( pt) set/ur le pg The rat population in a major metropolitan city is 87e t where t is mea- given by the formula n t sured in years since 99 and n t is measured in millions What was the rat population in 99? What is the rat population going to be in the year 7? ( pt) set/srw 9pg The half-life of Palladium- is days After days a sample of Palladium- has been reduced to a mass of 7 mg What was the initial mass (in mg) of the sample? What is the mass 6 weeks after the start? 5( pt) set/srw 3pg If dollars is invested in a bank account at an interest rate of 6 per cent per year, find the amount in the bank after years if interest is compounded annually Find the amount in the bank after years if interest is compounded quaterly Find the amount in the bank after years if interest is compounded monthly Finally, find the amount in the bank after years if interest is compounded continuously 6( pt) set/srm srw pg The doubling period of a baterial population is minutes At time t minutes, the baterial population was 9 For some constant A, the formula for the population is p t Ae kt where k ln What was the initial population at time t? Find the size of the baterial population after 5 hours 7( pt) set/srw 5 pg The 96 San Francisco earthquake had a magnitude of 83 on the Richter scale At the same time in South America there was an eathquake with magnitude 3 that caused only minor damage How many times more intense was the San Francisco earthquake than the South American one? The magnitude M on the Richter scale of an earthquake as a function of its intensity I is given by I M log! I " where I is some fied reference level of intensity 8( pt) set/golden-mathspring--p-8pg Human hair from a grave in Africa proved to have only 5 of the carbon of living tissue When was the body buried? See Problem 3 of Section 75 of the course tet The body was buried about years ago 9( pt) set/golden-mathspring--p-9pg Newton s Law of Cooling states that the rate at which an object cools is proportional to the difference in temperature between the object and the surrounding medium Thus, if an object is taken from an oven at 3# F and left to cool in a room at 7# F, its temperature T after t hours will satisfy the differential equation dt k T 7 dt If the temperature fell to 9# F in 6 hour(s), what will it be after hour(s)? After hour(s), the temperature will be # F ( pt) set/golden-mathspring--p-pg Inflation between 977 and 98 ran at about 5 per year On this basis, what would you epect a car that would have cost $9 in 977 to cost in 98?

5 ( pt) set/golden-mathspring--p-pg Use the fact that e lim h h h to find the following limits: (a) lim 6 = (b) lim 3 = n n 8 (c) lim n! = n " (d) lim n! n 6 n " n ( pt) set/golden-mathspring--p-3pg Solve the following differential equation: = y ytan sec Instruction: Name your integration constant C 3( pt) set/golden-mathspring--p-pg A tank initially contains gallons of brine, with 5 pounds of salt in solution Brine containing pounds of salt per gallon is entering the tank at the rate of gallons per minute and is flowing out at the same rate If the miture in the tank is kept uniform by constant stirring, find the amount of salt in the tank at the end of minutes Amount of salt after minutes: pound(s) ( pt) set/sc3 6 6apg Let f $ tan f NOTE: The WeBWorK system will accept arctan but not tan as the inverse of tan 5( pt) set/golden-mathspring--p-5pg Find the current I as a function of time for the circuit in the following figure if the switch S is closed and I at t, where E 5 volt(s), L 5 henry(s) and R ohm(s) (Click on image for a larger view ) 6( pt) set/golden-mathspring--p-6pg Megan bailed out of her plane at an altitude of 8 feet, fell freely for 5 seconds, and then opened her parachute Assume that the drag coefficients are a for a fee fall and a 6 with a parachute When did she land? It takes Megan about reach the ground seconds to

6 Shawn Harrison WW Prob Lib Math -, Fall 3 WeBWorK assignment 3 due 9/6/3 at 6: PM ( pt) set3/bertram mathspring3 p-pg Find the following values (try it without your calculator!): (a) cos sin 3 & (b) tan sec 3 & (c) sin cos π 6 & ( pt) set3/sc3 6 6apg Let f $ tan f NOTE: The WeBWorK system will accept arctan but not tan as the inverse of tan 3( pt) set3/sc3 6 3apg Let f 7sin sin f NOTE: The webwork system will accept arcsin and not sin as the inverse of sin ( pt) set3/bertram mathspring3 p-5pg Find the following derivatives (for suitable values of ): (a) d sin ln & & (b) d (c) d (' (d) d sinh ln & & tan & tanh & CAREFUL! WeBWorK does not recognize inverse hyperbolic functions You have to enter the answer using its equivalent epression with logarithms (see p 36) 5( pt) set3/bertram mathspring3 p-6pg Find the following integrals: (a) ) (b) ) t dt t dt t (c) ) t* dt t + (d) ) (e) ) t dt t t dt CAREFUL! WeBWorK does not recognize inverse hyperbolic functions and inverse secant function You have to enter the answer using its equivalent epression with logarithms (see p 36) and use the relationship between arcsec and arccos 6( pt) set3/golden-mathspring--p-pg Evaluate the integral: π sinθ cos θ dθ 7( pt) set3/golden-mathspring--p3-pg Perform the following integration: e sec e C 8( pt) set3/golden-mathspring--p-pg Evaluate the integral: 9( pt) set3/golden-mathspring--p-pg Suppose y sinh Find D y D y ( pt) set3/golden-mathspring--p-3pg Suppose y ln coth Find D y D y ( pt) set3/golden-mathspring--p-5pg The curve y sinh,,, is revolved about the -ais Find the area of the resulting surface

7 Shawn Harrison WW Prob Lib Math -, Fall 3 WeBWorK assignment due /8/3 at 6: PM ( pt) set/bertram mathspring3 p-pg Let a be a fied positive number Find the indefinite integrals: (a) ) cos a sin* + (b) ) cos sin & a ( pt) set/golden-mathspring--p3-pg Perform the following integration: + C + C 9 C 3( pt) set/golden-mathspring--p3-5pg Perform the following integration: 3 C ( pt) set/golden-mathspring--p3-6pg Perform the following integration: 5( pt) set/golden-mathspring--p3-7pg Perform the following integration: cos 3 C 6( pt) set/golden-mathspring--p3-pg Evaluate the following integral: L cos mπ nπ cos L L L where m - n and m, n are integers 7( pt) set/golden-mathspring--p3-pg Evaluate the following integral: t t dt 8( pt) set/golden-mathspring--p3-3pg Perform the following integration: sin cos 5 cos C 5 C

8 Shawn Harrison WW Prob Lib Math -, Fall 3 WeBWorK assignment 5 due //3 at 6: PM ( pt) set5/golden-mathspring--p-pg Use integration by parts to evaluate the following integral: arctan5 C ( pt) set5/golden-mathspring--p-7pg Use the method of partial fraction decomposition to perform the following integration: 6 C 3( pt) set5/golden-mathspring--p-9pg Use the method of partial fraction decomposition to perform the following integration: 6 C ( pt) set5/golden-mathspring--p-3pg Find the following limit using l Hopital s Rule: lim ) t cost dt Enter the word infinity if the answer is 5( pt) set5/golden-mathspring--p-9pg Find the following limit: lim 6( pt) set5/golden-mathspring--p-pg Evaluate the following improper integral: ln e If the integral diverges, enter diverge as answer

9 Shawn Harrison WW Prob Lib Math -, Fall 3 WeBWorK assignment 6 due /3/3 at 6: PM! ( pt) set6/math spring3 bertram set7 ppg Find the following improper integrals If the integral diverges, write I: (a) ) (b) ) ( pt) set6/math spring3 bertram set7 p3pg Find the following integrals If the integral diverges, write I: (a) ) (b) ) (c) ) 3( pt) set6/math spring3 bertram set7 p6pg Find the limit of each series If it diverges, write I (a) / / (b) / (c) k3 k 7k ( pt) set6/golden-mathspring--p5-5pg A ball is dropped from a height of 93 feet Each time it hits the floor, it rebounds to its previous 3 height Find the total distance it travels before coming to rest feet 5( pt) set6/golden-mathspring--p5-pg Decide the convergence or divergence of the following series: k3 k k " (Enter convergent or divergent ) 6( pt) set6/golden-mathspring--p5-8pg Use the Integral Test to decide the convergence or divergence of the following series: k k3 e k (Enter converge or diverge )

10 Shawn Harrison WW Prob Lib Math -, Fall 3 WeBWorK assignment 7 due //3 at 6: PM ( pt) set7/golden-mathspring--p6-pg Determine the convergence or divergence of the following series A convergent B divergent n3 n n ( pt) set7/golden-mathspring--p6-pg Determine the convergence or divergence of the following series n3 A convergent B divergent n cos! n"65 ( pt) set7/golden-mathspring--p6-pg Determine the convergence or divergence of the following series A convergent B divergent n3 3 k k k! 3( pt) set7/golden-mathspring--p6-3pg Determine the convergence or divergence of the following series A convergent B divergent 5 n n3 n! 5( pt) set7/golden-mathspring--p6-5pg Determine whether the following series is n3 n 5n A absolutely convergent B conditionally convergent C divergent 6( pt) set7/golden-mathspring--p6-6pg Determine whether the following series is n3 n n A absolutely convergent B conditionally convergent C divergent

11 Shawn Harrison WW Prob Lib Math -, Fall 3 WeBWorK assignment 8 due /7/3 at 6: PM 9 ( pt) set8/golden-mathspring--p6-7pg Determine whether the following series is n3 n sinn n n A absolutely convergent B conditionally convergent C divergent ( pt) set8/golden-mathspring--p6-8pg Find the convergence set of the given power series: n n n! n3 The above series converges for Enter infinity for and -infinity for 3( pt) set8/golden-mathspring--p6-9pg Find the convergence set of the given power series: n n n3 The above series converges for,, Enter infinity for and -infinity for ( pt) set8/golden-mathspring--p6-pg A famous sequence f n, called the Fibonacci Sequence after Leonardo Fibonacci, who introduced it around AD, is defined by the recursion formula f f f n f n f n Find the radius of convergence of n3 f n n Radius of convergence: 5( pt) set8/math spring3 bertram set8 ppg If the series converges, find its limit If it diverges, write I (a) k3 k k!!! / / (b) k3 k! k!! 7 / (c) k3 * + k k!!! 8 / 6( pt) set8/math spring3 bertram set8 p3pg Find the convergence sets for the following power series: Use the following notions in the a b c ; A B :; C < D E F (a) k3 * k + k ConvergenceSet : (b) k3 k k k ConvergenceSet : (c) k3 k * k +! k ConvergenceSet :,,, (d) * k +! k3 k ConvergenceSet k = : >