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 -∞.
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 $-\infty$.
Solution
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 \(20\).