The correct option is A π/180 We know , lim _ x→ 0 sin x #160; x #160; =1 ⇒lim _ x→ 0 sin x #160; x #160; =lim _ x→ 0 sin (x ...

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Substitution Method to Remove Indeterminate Form

limx → 0 sinx...

Question

$lim x \to 0 \frac{sin x^{0}}{x} =$

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\frac{π}{180}

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180

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Solution

The correct option is A $\frac{π}{180}$
We know , ${lim}_{x \to 0} \frac{sin x}{x} = 1$
$\Rightarrow {lim}_{x \to 0} \frac{sin x}{x} = {lim}_{x \to 0} \frac{sin (x . \frac{π}{180})}{x} = {lim}_{x \to 0} \frac{π}{180} \times \frac{sin (\frac{x π}{180})}{\frac{x π}{180}}$
Let $\frac{x π}{180} = k$ $\Rightarrow$ as $x \to 0, k \to 0$
${lim}_{x \to 0} \frac{π}{180} \times \frac{sin (\frac{x π}{180})}{\frac{x π}{180}} = {lim}_{k \to 0} \frac{π}{180} \times \frac{sin k}{k} = \frac{π}{180} \times 1 = \frac{π}{180}$

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