1225FormA

10. Let f be a function such that x 2 − 1 ≤ f ( x ) ≤ 1 − x 2 for all x in ( − 1 , 1) and assume that f is defined everywhere. Which of the following statements MUST be TRUE ?

(A) lim x → 0

f ( x ) does not exist.

(B) f (1) = 0. (C) lim x → 0

f ( x ) = 1.

(D) lim

f ( x ) = 0.

x →− 1 +

11. Consider the graph of y = f ( x ) given below:

y

3

x

− 1 2

y = L ( x )

y = f ( x )

Suppose that L is the linearization of f at x = 3. Which of the following MUST be FALSE ?

(A) If we use x 1 = 3 as the initial approximation of Newton’s Method, then L ( x 2 ) = 0 (where x 2 is the second approximation of Newton’s method). (B) L also represents the linearization of f at a = − 1 2 .

(C) f ′ (3) = L ( x ) . (D) The tangent line to the graph of y = f ( x ) at x = 3 is y = L ( x ). 12. Given f ( x ) = Z 3 x 2 sin 4 ( t ) dt , find f ′ ( x ). (A) f ′ ( x ) = − 2 x sin 4 ( x 2 ) (B) f ′ ( x ) = − sin 4 ( x 2 ) d dx

(C) f ′ ( x ) = − 4 sin 3 ( x 2 ) cos( x 2 ) (D) f ′ ( x ) = − 8 x sin 3 ( x 2 ) cos( x 2 )

Page 6 of 7 — Form A