Question

find the limit:
lim_{x
ightarrow100}\frac{sqrt{x}-10}{x - 100}
give an exact answer or keep at least three decimal place
question help: video message instructor

Explanation:

Step1: Rationalize the numerator

Multiply the fraction by $\frac{\sqrt{x}+10}{\sqrt{x}+10}$.

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Using the difference - of - squares formula $(a - b)(a + b)=a^{2}-b^{2}$, we have $(\sqrt{x}-10)(\sqrt{x}+10)=x - 100$. So the expression becomes $\lim_{x
ightarrow100}\frac{x - 100}{(x - 100)(\sqrt{x}+10)}$.

Step2: Simplify the fraction

Cancel out the common factor $(x - 100)$ in the numerator and denominator.

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Step3: Evaluate the limit

Substitute $x = 100$ into $\frac{1}{\sqrt{x}+10}$.

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Answer:

$0.05$