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Step-by-step Solution

Find the limit of $\frac{\sqrt{x+3}-2}{x^2-1}$ as $x$ approaches $1$

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Answer

indeterminate

Step-by-step explanation

Problem to solve:

$\lim_{x\to1}\left(\frac{\sqrt{x+3}-2}{x^2-1}\right)$
1

Rewrite the difference of squares $x^2-1$ as the product of two conjugated binomials

$\lim_{x\to1}\left(\frac{\sqrt{x+3}-2}{\left(x+1\right)\left(x-1\right)}\right)$
2

Simplifying

indeterminate

Answer

indeterminate

Problem Analysis

$\lim_{x\to1}\left(\frac{\sqrt{x+3}-2}{x^2-1}\right)$

Main topic:

Limits

Time to solve it:

~ 0.1 seconds