All work must be shown in this course for full credit. Unsupported answers may receive NO credit.

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1 AP Calculus.1 Worksheet Day 1 All work must be shown in this course for full credit. Unsupported answers may receive NO credit. 1. The only way to guarantee the eistence of a it is to algebraically prove it. Describe the different ways you can investigate the eistence of a it.. Using words, eplain what is meant by the epression f ( q) = T. qc 3. How can you find the average speed of an object? 4. One way to find the instantaneous speed of an object is to find the average speed between a given time and a time that is h seconds later. Read eample on page 59 of your tetbook. Describe how to find the instantaneous speed of an object using this method. 5. Suppose an object moves along the -ais with it s position function given by () t = 5t + 7t, where t is measured in seconds. a) What is the average speed from t = to t = 4 seconds? b) How fast is the object moving at eactly t = 4 seconds? 6. Complete the following questions from your tetbook: page 68 #63 and When asked to evaluate the it of a function, what should be done first? 8. Evaluate the following its by using direct substitution. a) sec b) + 4 4

2 9. Complete the following questions from your tetbook: pages 66 67: #5, 7, 10, 13, 14, and If a it does not eist, there are 3 possible reasons why. List all three possible reasons why a it may not eist. 11. If f ln for 0 ln for 4, then f 1. If f ( ) ì 3+ 1, < = ï í 5, ³ ï ïî + 1 find f ( ) +, if it eists. If it does not eist, eplain why. 13. Complete the following questions from the tetbook: page #15, 16, 17, 9, 30, 38, 39, 4, 44, 51, 5, 53, 57

3 AP Calculus.1 Worksheet Day All work must be shown in this course for full credit. Unsupported answers may receive NO credit. 1. When evaluating its, what does it mean if direct substitution gives you 7 0?. When evaluating its, what does it mean if direct substitution gives you 0 0? 3. What are the methods (options) for dealing with the result in question? 4. Evaluate the following its algebraically: a) b) c) tan 0 d) 4 sin Complete the following questions from the tetbook: page 66 #18 8. f 1, then 6. If f f 0 0

4 7. If a 0, then a a a Find , if it eists. A) 1 B) 1 C) D) 5 E) does not eist 9. Complete the following questions from the tetbook: page 68 # Evaluate the following its algebraically: a) sin 5 0 b) c) 3 0 d) sin 0 5 e) sin f) 1

5 11. Evaluate the following its algebraically: a) b) Evaluate ( ) + h -. h 0 h : h is going to 0 not so treat this as if h is the variable your final answer will have a in it.

6 AP Calculus. Worksheet All work must be shown in this course for full credit. Unsupported answers may receive NO credit. 1. Sketch a function that satisfies the stated conditions. Include any asymptotes. f f 1 f 5 5 f 1 f f 0 f. Sketch a function that satisfies the stated conditions. Include any asymptotes. f 1 f f 4 f 4 f 3. Answer the following questions: a) How do you find horizontal asymptotes? b) Which one of the parent functions have horizontal asymptotes? List the function(s) and asymptote(s) c) How do you find vertical asymptotes? d) Which one of the parent functions have vertical asymptotes? List the function(s) and asymptote(s) e) When must you look for oblique (slanted) asymptotes? How do you find them? 4. Eplain why there is no value L for which sin = L.

7 5. Let f ( ) cos =. a) Find the domain and range of f. b) Is f even, odd, or neither? Justify your response. c) Find f ( ). Give a reason for your answer. 6. If k is a positive integer, then e k? Eplain your answer. 7. Evaluate the following its: a) n 3 4n 10000n b) n n 3 3n 5 n n 1 3 c) 5 = d) sin sin e) f) cos 1 ( ) Investigate the following its to determine the value of each: 3 1 and Complete the following questions from the tetbook: page 76 #3, 7, 15, 0, 5, 7, 30, 39, 41, 4, 43, 53, and 54

8 AP Calculus.3 Worksheet All work must be shown in this course for full credit. Unsupported answers may receive NO credit. 1. What is the definition of continuity?. Sketch a possible graph for each function described. a) f (5) eists, but f ( ) does not eist. b) The f ( ) 5 5 eists, but f (5) does not eist. 3. Let f ( ) ìï - a < ; = ï í. Find all values of a that make f continuous at. ï ïî 4- ; ³ Using the definition of continuity, justify your response. 4. If 5 7 if f, and if f is continuous at =, then k =? Justify your response. k 3 if 5. Complete the following questions from your tetbook: page 85 #47 and 48

9 6. Let f be the function defined by the following: For what values of is f NOT continuous? f sin, 0, 0 1, 1 3, 7. If the function f is continuous for all real numbers and if f 4, when, then f ( ) = 8. Let f be the function given by f 1 4 a. For what positive values of a is f continuous for all real numbers? A) None B) 1 only C) only D) 4 only E) 1 and Let h( ) = a) Find the domain of g (). b) Find the g c ( ) for all values of c where g () is not defined. c) Find any horizontal asymptotes and justify your response. d) Find any vertical asymptotes and justify your response. e) Write an etension to the function so that g () is continuous at =.

10 10. Complete the following questions from the tetbook: page #1, 7, 10, 11 18, 8, 9, 58, Without using a picture, give a written eplanation of why the function f ( ) 4 3 = - + has a zero in the interval [, 4]. ìï 3-4, if 1. Let h( ) = ï í. ï ïî 5+ 4, if > a) What is h (0)? b) What is h (4)? c) Is there a value of such that h () = 10? Eplain why this result does not contradict the IVT.

11 AP Calculus.4 Worksheet All work must be shown in this course for full credit. Unsupported answers may receive NO credit. 1. What is a difference quotient?. How do you find the slope of a curve (aka slope of the tangent line to a curve) when = a? 3. What is a normal line? 4. What is the difference between the AVERAGE RATE OF CHANGE and INSTANTANEOUS RATE OF CHANGE? 3 5. Let f ( ) =. a) Write an epression for f (a + h). b) Find the slope of the curve at = a. c) When does the slope equal 1? d) Write the equation of the tangent line to the curve at = 4 e) Write the equation of the normal line to the curve at = 4

12 6. Let g( ) = a) Find the average rate of change from = 4 to = 9. b) Find the instantaneous rate of change at = 9. c) Write the equation of the tangent line when = 9 d) Write the equation of the normal line when = Complete the following from the tetbook: page 9 93 #3, 6, 7, 11, 1, 3, 5, 9, 38, and You should also begin reviewing for your chapter test: page #1 9, 31, 33, 35, 39, 40, 43 49, 5. This isn t due until the day of your eam.