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Standard XII

Physics

Introduction

lim x → 0 sin...

Question

$\lim_{x \to 0} \frac{\sin x^{0}}{x}$

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Solution

We know that $x ° = \frac{π}{180} x$ .

$∴ \lim_{x \to 0} \frac{\sin x^{0}}{x} = \lim_{x \to 0} \frac{\sin \frac{π}{180} x}{x} = \lim_{x \to 0} \frac{\sin (\frac{π}{180} x)}{(\frac{π}{180} x)} \times \frac{π}{180} = \frac{π}{180} \times 1 = \frac{π}{180}$

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Similar questions

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

is equal to -

\lim_{x \to 0} \frac{\sin x^{0}}{x}

is equal to

(a) 1
(b) π
(c) x
(d) π/180

Q. STATEMENT-1 :

{lim}_{x \to \infty} (\frac{1^{2}}{x^{3}} + \frac{2^{2}}{x^{3}} + \frac{3^{2}}{x^{3}} + . . . . . . . + \frac{x^{2}}{x^{3}}) = lim x \to \infty \frac{1^{2}}{x^{3}} + lim x \to \infty \frac{2^{2}}{x^{3}} + . . . . . + lim x \to \infty \frac{x^{2}}{x^{3}} = 0

STATEMENT-2 :

{lim}_{x \to a} (f_{1} (x) + f_{2} (x) + . . . . . + f_{n} (x)) = {lim}_{x \to a} f_{1} (x) + {lim}_{x \to a} f_{2} (x) + . . . . + {lim}_{x \to a} f_{n} (x)

, where

n \in N .

If both $lim x \to a f (x)$ and $lim x \to a g (x)$ and exist finitely and $lim x \to a g (x) = 0$ , then
$lim x \to a \frac{f (x)}{g (x)} = \frac{lim x \to a f (x)}{lim x \to a g (x)}$

$lim x \to a [f (x) + g (x)] = lim x \to a f (x) + lim x \to a g (x)$
is valid if $lim x \to a f (x)$ does not exists?

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limx→0sin x0x

We know that x°=π180x. ∴limx→0 sin x0x=limx→0 sin π180xx=limx→0 sin π180xπ180x×π180=π180×1=π180

$\lim_{x \to 0} \frac{\sin x^{0}}{x}$

We know that $x ° = \frac{π}{180} x$ .

$∴ \lim_{x \to 0} \frac{\sin x^{0}}{x} = \lim_{x \to 0} \frac{\sin \frac{π}{180} x}{x} = \lim_{x \to 0} \frac{\sin (\frac{π}{180} x)}{(\frac{π}{180} x)} \times \frac{π}{180} = \frac{π}{180} \times 1 = \frac{π}{180}$