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Limits (p-1) — Maths (commerce) STD 11 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 11 Commerce / ArtsMaths (commerce)Limits (p-1)1 Mark
Question
Evaluate the following limits:

$\lim _{x \rightarrow 3}\left[\frac{\sqrt{x+6}}{x}\right]$

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Answer

$\begin{aligned} \lim _{x \rightarrow 3}\left[\frac{\sqrt{x+6}}{x}\right] & =\frac{\lim _{x \rightarrow 3} \sqrt{x+6}}{\lim _{x \rightarrow 3} x} \\ & =\frac{\sqrt{3+6}}{3} \\ & =\frac{\sqrt{9}}{3} \\ & =\frac{3}{3} \\ & =1\end{aligned}$

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