Respuesta :

Explanation:

Limit of the function:

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

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

a)

[tex]\lim _{x\to-\infty}(2x^3-2x)=-\infty[/tex]

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

b)

[tex]\lim _{x\to\infty}(-2x^4+6x^3-2x)=-\infty[/tex]

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

This statement is true.

c)

[tex]\lim _{x\to\infty}(9x^5-6x^3-x)=-\infty[/tex]

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

So, This statement is false.

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