 # Simplify. lim_(xrightarrow 1)(sqrt(x-1))/(x^2 +x) and +lim_(xrightarrow 1)(sqrt(x-1))/(x^2 +x) comAttitRize8 2022-07-27 Answered
Simplify.
$\underset{x\to 1}{lim}\frac{\sqrt{x-1}}{{x}^{2}+x}$and$\underset{x\to 1}{lim}+\frac{\sqrt{x-1}}{{x}^{2}+x}$
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in order for to exist then both and $\underset{x\to 1}{lim}-\frac{\sqrt{x-1}}{{x}^{2}+x}$ must exist. Since $\frac{\sqrt{x-1}}{{x}^{2}+x}$ is undefined for x < 1 then doesnot exist. however does exist since it is a one sided limit, the limit is zero.
###### Not exactly what you’re looking for? Almintas2l
$\underset{x\to 1}{lim}﻿\frac{\sqrt{x-1}}{{x}^{2}+x}=\frac{\sqrt{1-1}}{1+1}=0$
$\underset{x\to 1}{lim}-\frac{\sqrt{x-1}}{{x}^{2}+x}=\underset{x\to 1}{lim}+\frac{\sqrt{x-1}}{{x}^{2}+x}=0=\underset{x\to 1}{lim}\frac{\sqrt{x-1}}{{x}^{2}+x}$