Question

Using the squeeze theorem, find lim(x → 3) f(x) given that 4 - |x - 3| ≤ f(x) ≤ 4 |x - 3|.

A) lim(x → 3) f(x) = 4
B) lim(x → 3) f(x) = 0
C) lim(x → 3) f(x) = [infinity]
D) lim(x → 3) f(x) = -[infinity]

Answer 1

Using the squeeze theorem, the limit of f(x) as x approaches 3 is 4.

Step-by-step explanation:

To find the limit using the squeeze theorem, we need to determine the limits of the two functions that act as bounds for f(x). The lower bound is 4 - |x - 3|, and the upper bound is 4 |x - 3|. As x approaches 3, both of these functions converge to 4. Therefore, by the squeeze theorem, the limit of f(x) as x approaches 3 is also 4.