Question

assignment 3: problem 20 (1 point)
suppose
4x - 20 ≤ f(x) ≤ x² - 4x - 4
use this to compute the following limit.
lim(x→4) f(x)
answer:
what theorem did you use to arrive at your answer?
answer:
note: you can earn partial credit on this problem.

Explanation:

Step1: Find left - hand limit

Find $\lim_{x
ightarrow4}(4x - 20)$. Substitute $x = 4$ into $4x-20$:
$\lim_{x
ightarrow4}(4x - 20)=4\times4-20=16 - 20=-4$.

Step2: Find right - hand limit

Find $\lim_{x
ightarrow4}(x^{2}-4x - 4)$. Substitute $x = 4$ into $x^{2}-4x - 4$:
$\lim_{x
ightarrow4}(x^{2}-4x - 4)=4^{2}-4\times4-4=16 - 16-4=-4$.

Step3: Apply Squeeze Theorem

Since $4x - 20\leq f(x)\leq x^{2}-4x - 4$ and $\lim_{x
ightarrow4}(4x - 20)=\lim_{x
ightarrow4}(x^{2}-4x - 4)=-4$, by the Squeeze Theorem, $\lim_{x
ightarrow4}f(x)=-4$.

Answer:

-4
Squeeze Theorem