Explain your answers using the continuity property of the addition, subtraction, multiplication, and division.

Brennan Flores
2021-11-09
Answered

Find the following:

$\underset{x\to -2}{lim}(\frac{1}{{x}^{2}}+\frac{1}{{x}^{3}+4})$

Explain your answers using the continuity property of the addition, subtraction, multiplication, and division.

Explain your answers using the continuity property of the addition, subtraction, multiplication, and division.

You can still ask an expert for help

lamusesamuset

Answered 2021-11-10
Author has **93** answers

Given,

$\underset{x\to -2}{lim}(\frac{1}{{x}^{2}}+\frac{1}{{x}^{3}+4})$

By addition property of limits

we know$\underset{x\to a}{lim}[f\left(x\right)+g\left(x\right)]$

$=\underset{x\to a}{lim}f\left(x\right)+\underset{x\to a}{lim}g\left(x\right)$

Therefore

$\underset{x\to -2}{lim}(\frac{1}{{x}^{2}}+\frac{1}{{x}^{3}+4})=\underset{x\to -2}{lim}\frac{1}{{x}^{2}}+\underset{x\to -2}{lim}\frac{1}{{x}^{3}+4}$

$=\underset{x\to -2}{lim}\frac{1}{{x}^{2}}+\underset{x\to -2}{lim}\frac{1}{{x}^{3}+4}$

$=\frac{1}{4}+\frac{1}{{(-2)}^{3}+4}$

$=\frac{1}{4}+\frac{1}{-8+4}$

$=\frac{1}{4}-\frac{1}{4}=0$

By addition property of limits

we know

Therefore

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