The correct option is B π180 lim_x → 0 sinx^ ∘ x = lim_x → 0 sin( π #160; 180x) x = lim_x → 0π180π180·sin( π180x)x = π180lim_x → 0s ...

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Substitution Method to Remove Indeterminate Form

Solve limx ...

Question

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

1

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\frac{π}{180}

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Solution

The correct option is B $\frac{π}{180}$
$lim x \to 0 \frac{sin x^{\circ}}{x}$

= $lim x \to 0 \frac{sin (\frac{π}{180} x)}{x}$

$= lim x \to 0 \frac{\frac{π}{180}}{\frac{π}{180}} \cdot \frac{sin (\frac{π}{180 x})}{x}$

$= \frac{π}{180} lim x \to 0 \frac{sin (\frac{π}{180 x})}{\frac{π}{180 x}}$

= $\frac{π}{180} .1$

$= \frac{π}{180}$

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