Evaluate the following limit: _ x 0 x^2 ^2 - Vidyadip

Question

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{x}^2}{\sin\text{x}^2}$

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Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\text{x}^2}{\sin\text{x}^2}$
$=\frac{1}{\lim\limits_{\text{x}\rightarrow0}\frac{\sin\text{x}^2}{\text{x}^2}}{}$ $\Big[\because\ \lim\limits_{\text{x}\rightarrow0}\frac{\sin\text{x}}{\text{x}}=1\Big]$
$=\frac11$
$=1$

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