AP Calculus AB Chapter 2 Test September 20, 2014 Show all your work.

Transcription

1 Name AP Calculus AB Chapter Test September 0, 014 Show all your work. 1. Find lim 5 7 A. 5/ B. -5/ C. 0 D. The limit does not eist because the function increases without bound. E. The limit does not eist because the function decreases without bound.. Find the average rate of change of the function f ) sec ( over the interval 0, A. B. C. D. E. -

2 . Consider the piecewise function 4 a,, For what value (or values) of a is f () a continuous function? A. -1/ B. 5/ C. 9/ D. 7 E. f () is a continuous function for all values of a. For problems 4 & 5, consider the function 4. What is lim? 0 A. - B. 0 C. D. 5 E. The limit does not eist. 5sin 5. What is lim? A. - B. C. 5 D. The limit does not eist because the function increases without bound. E. The limit does not eist because the function decreases without bound.

3 6. Below, sketch one possible graph of the function f () that has the following features: The domain of f is all real numbers ecept =. lim eists and f (4) is defined, but lim f (4) 4 4 lim eists and lim eists, but lim lim There are horizontal asymptotes at y = 0 and y = Based on the features given in problem 6, is f () a continuous function? Eplain why or why not.

4 For questions 8 and 9, consider the function 7 8. What are all of the horizontal asymptotes? A. y 1 only B. y 1 only C. y 1 and y 1 D. y 0 and y 1 E. y 0 and y 1 9. What are all of the vertical asymptotes?

5 10. Maria Louise wants to determine if g( ) is a left-end behavior model for e. If g() is an end behavior model for f(), which of the following would be true? e A. lim 1 e B. lim 0 e C. lim 0 e D. lim 1 E. None of the above 11. After learning about Søren Kierkegaard in philosophy class, you ve decided to become a nihilist and to that end, you cut your philosophy class. Since this is the first time (this year) that an AP student has cut a class, Mr. Lottmann calls you into his office. He tells you that when he was your age, he also cut a class once (Intro to Pajamas-Making) and his principal (Mr. Warren) offered him a deal that he is now going to offer to you. Mr. Lottmann says, Is there any number that will make that equal 5? Use the intermediate value theorem to answer the question. Answer correctly, and I ll only give you a week of lunch detention. Answer wrong and one day, you ll have to be principal of this school. Be careful to show all your work! Looks like Mr. Lottmann means business!!

6 1. A faraway planet named Tonmant-L, is facing severe and devastating weather phenomena due to its inhabitant polluting the air and ignoring the warnings about global climate change for decades. Because of the methane ice caps at the planets poles are melting, the water levels of the planet s largest ocean, Cupcakia, are rising. Scientists in the shore town of Shoretownville have determined that since the beginning of the year, the depth of the ocean in their town is given by the function t d ( t) 5t, where d is measured in meters and t is measured in days since the 100 beginning of the year. On the 100 th day of the year, what is the rate of change (in meters per day) of the depth of the ocean in Shoretownville?

7 1) Consider the function 5. a) Find the slope of f() when = -1. b) Write an equation of the line tangent to f() at = -1. c) Write an equation of the line normal to f() at = -1.