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2

1.16

1.28

1.12

1.04

( x sec2 x dx =

x tan x + C

sec2x + 2 sec2 x tan x + C

x tan x – ln |cos x| + C

x tan x + ln |cos x| + C

The length of the curve determined by the equations x = t2 and y = t from t = 0 to t = 4 is

A point moves in a straight line so that its distance at time t from a fixed point of the line is 4t2 -5t. What is the total distance covered by the point between 3rd and 6th seconds?

13

43

53

23

93

Consider the curve in the xy-plane represented by x = et and y = te-t for t ( 0. The slope of the line tangent to the curve at the point where x = 3 is

2.075

0.482

–0. 037

–0.066

–0. 005

1/4

3/4

1/2

-3/4

-1/4

The number of bacteria in a culture is growing at a rate of 6000e3t/4 per unit of time t. At t = 0, the number of bacteria present was 8000. Find the number present at t = 4.

7500e2

2000e2

6000e5

1400 e2

8000e3

None of the above

None of the above

28

20

16

24

32

None of the above

17/2

5

15/2

nonexistent

2(e – 1)

4(e – 1)

Which of the following represents the graph of the polar curve r = 2 sec(?

0

1

n – 1

n

n + 1

1/12

-1/12

0

1

Undefined

There is no minimum value for ‘a’

e

1

6.103

3.124

4.223

2.498

5.126

This test contains twenty questions on Derivatives and Applications of derivatives, Vector valued functions, Integrals, Application of Integrals. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number. Wherever appeared, lnx represents the natural logarithm of x with base e. Sometimes, the options may not contain exact numerical value of an answer. In that case, select best approximation to the numerical value you got. After examining the form of the choices, decide the best of the choices given.

AP Calculus BC Test 8 Derivatives and Applications of derivatives Vector valued functions Integrals Application of Integrals

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