Question

Hi I need help with this practice question from my calculus prep guide

Answer 1

Explanation:

Limit of the function:

Limit is the approximate value of the function at a defined value of x.

$\begin{gathered} \lim _{x\to a}f(x)=L \\ As\text{ }x\rightarrow a\text{ then, f(x)}\rightarrow L \end{gathered}$

a)

$\lim _{x\to-\infty}(2x^3-2x)=-\infty$

This limit is true. As x approaches negative infinity the function is also approached to negative infinity.

b)

$\lim _{x\to\infty}(-2x^4+6x^3-2x)=-\infty$

As x tends to infinity. The functions tend to have negative infinity.

This statement is true.

c)

$\lim _{x\to\infty}(9x^5-6x^3-x)=-\infty$

When x tends to infinity, the function will also go to infinity.

So, This statement is false.