Questions: Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value. lim (x -> 10) (x^2-100)/(x-10) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. lim (x -> 10) (x^2-100)/(x-10)= (Simplify your answer.) B. The limit does not exist and is neither ∞ nor -∞.

Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value.

lim (x -> 10) (x^2-100)/(x-10)

Select the correct choice below and, if necessary, fill in the answer box within your choice. A. lim (x -> 10) (x^2-100)/(x-10)= 
(Simplify your answer.) B. The limit does not exist and is neither ∞ nor -∞.
Transcript text: Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value. \[ \lim _{x \rightarrow 10} \frac{x^{2}-100}{x-10} \] Select the correct choice below and, if necessary, fill in the answer box within your choice. A. $\lim _{x \rightarrow 10} \frac{x^{2}-100}{x-10}=$ $\square$ (Simplify your answer.) B. The limit does not exist and is neither $\infty$ nor $-\infty$.
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Solution

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Solution Steps

Step 1: Simplify the Rational Function

We simplify the given function \(\frac{x^{2} - 100}{x - 10}\).

Step 2: Evaluate the Limit

After simplification, we directly substitute \(x = 10\) into the simplified function to find the limit. \[\lim_{x \to 10} \frac{x^{2} - 100}{x - 10} = 20\]

Final Answer

The limit of the function as \(x\) approaches \(10\) is \(20\).

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