Question

Find the limit of the function algebraically.

limit as x approaches negative ten of quantity x squared minus one hundred divided by quantity x plus ten.

-10
-20
Does not exist
1

Answer 1

$\bf \lim\limits_{x\to -10}~\cfrac{x^2-100}{x+10}\implies \cfrac{\stackrel{\textit{difference of squares}}{x^2-10^2}}{x+10}\implies \cfrac{(x-10)(\underline{x+10})}{\underline{x+10}} \\\\\\ \lim\limits_{x\to -10}~x-10\implies \lim\limits_{x\to -10}~-10-10\implies -20$

Answer 2

The value of the limit of the function algebraically will be -20. Then the correct option is B.

What is the limit?

The value that approaches the output for the given input value. Limits are a very important tool in calculus.

The limit is given as,

$\displaystyle \lim_{x \to -10} \left ( \dfrac{x^2-100}{x+10} \right )$

Apply L'hospital rule, then we have

$\displaystyle \lim_{x \to -10} \left ( \dfrac{\dfrac{d}{dx}(x^2-100)}{\dfrac{d}{dx}(x+10)} \right )\\\displaystyle \lim_{x \to -10} \left ( \dfrac{2x}{1} \right )$

Put the limit, then we have

⇒ 2(-10)

⇒ -20

Then the correct option is B.

More about the limit link is given below.

https://brainly.com/question/8533149

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