LIMITS AND DERIVATIVES — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLIMITS AND DERIVATIVES1 Mark
Question
Find the limit: $\lim \limits_{x \rightarrow 2}\left[\frac{x^{2}-4}{x^{3}-4 x^{2}+4 x}\right]$
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Answer
Evaluating the function at 2, we get it of the form $\frac{0}{0}$ Therefore, we have, $\lim _{x \rightarrow 2} \frac{x^{2}-4}{x^{3}-4 x^{2}+4 x}=\lim _{x \rightarrow 2} \frac{(x+2)(x-2)}{x(x-2)^{2}}$ $=\lim _{x \rightarrow 2} \frac{(x+2)}{x(x-2)}=\frac{2+2}{2(2-2)}=\frac{4}{0}$ = $\infty$
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