1225FormA

3. Let f and g be two differentiable functions for all real values of x . The following table shows some values for f , f ′ , g , and g ′ .

f ′ ( x ) g ( x ) g ′ ( x )

x f ( x )

− 1 2 0 0 2 1

− 4 3

8 5

− 5

2

− 3 1 10

Evaluate the following at x = 2:

d dx

g ( x ) f ( x − 3)

5 4

(A)

(B) 3 (C) 7 (D) 12

4. A cylindrical tank with radius 10 feet is being filled with water at the rate of 300 ft 3 / min. How fast is the water level rising? Recall: The volume of a cylinder is given by V = πr 2 h , where r is the radius and h is the height of the cylinder.

3 π

(A)

ft / min

15 π 3 4 π

(B)

ft / min

(C)

ft / min

(D) Without more information about dr dt

, this problem cannot be solved.

5. Which of the following definite integrals is equal to the following expression?

n X i =1

+ 2

2

1 n

i n

lim n →∞

(A) Z

(B) Z

(C) Z

(D) Z

1

2

1

3

x 2 dx

x 2 dx

( x + 2) 2 dx

( x + 2) 2 dx

0

0

0

2

Page 3 of 7 — Form A