Two functions and are defined as follows

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Two functions

g

and

f

are defined as follows. Values of

g

near

x=2

: x | 1.9 | 1.99 | 2.01 | 2.1 g(x) | 3.12 | 3.01 | 2.99 | 2.88 Values of

f

near

u=3

: u | 2.9 | 2.99 | 3.01 | 3.1 f(u) | 7.04 | 7.0004 | 6.9996 | 6.96 Using the data, what is the best estimate of

\displaystyle \lim_{x\to 2} f\bigl(g(x)\bigr)

? (a)

7.04

(b)

7

(c)

6.96

(d)

9