1. ## limits

Consider the relationship involving g(x).

8x ≤ g(x) ≤ 4x^4 - 4x^2 + 8 for all x

Evaluate the following limit.

2. Originally Posted by zweevu
Consider the relationship involving g(x).

8x ≤ g(x) ≤ 4x^4 - 4x^2 + 8 for all x

Evaluate the following limit.

This is a straightforward application of the sandwich theorem.

Note that if

$8x \leq g(x) \leq 4x^4 - 4x^2 + 8$ for all $x$, then

$\lim_{x \to 1}8x \leq \lim_{x \to 1}g(x) \leq \lim_{x \to 1}(4x^4 - 4x^2 + 8)$

$8 \leq \lim_{x \to 1}g(x) \leq 8$.

What does this tell you about $\lim_{x \to 1}g(x)$?

3. Originally Posted by zweevu
Consider the relationship involving g(x).

8x ≤ g(x) ≤ 4x^4 - 4x^2 + 8 for all x

Evaluate the following limit.

Since g(x) lies between the other two functions of x for all x, evaluate the limits of the others and analyze the result.