Math  /  Calculus

QuestionEvaluate the following limit. Give an exact answer if the limit is a number. Otherwise, enter -\infty or \infty if the limit is infinite, or enter DNE if the limit does not exist in another way. limx8x+175x8=\lim _{x \rightarrow 8} \frac{\sqrt{x+17}-5}{x-8}= \square
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Studdy Solution
Evaluate the limit as xx approaches 8.
limx81x+17+5=18+17+5=125+5=15+5=110 \lim_{x \rightarrow 8} \frac{1}{\sqrt{x+17}+5} = \frac{1}{\sqrt{8+17}+5} = \frac{1}{\sqrt{25}+5} = \frac{1}{5+5} = \frac{1}{10}
The solution to the limit is:
110 \boxed{\frac{1}{10}}

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