The value of limx- 0-1-sin x-1-sin xx is

The value of nbsp;lim_x→ 0√(1+sin x) √(1 sin x)x lim_x→ 0(1+sin x) (1 sin x) (1+sin x)^23+(1+sin x)^13(1 sin x)^13+(1 sin x)^23.1x lim_x→ 01 (1+sin x)^23+(1+ ...

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Standard XII

Mathematics

Expansions to Remove Indeterminate Form

The value of ...

Question

The value of $lim x \to 0 \frac{\sqrt[3]{1 + sin x} - \sqrt[3]{1 - sin x}}{x}$ is

\frac{2}{3}

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same as the value of

lim x \to 0 \frac{sin 2 x}{tan 3 x}

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same as the value of

lim x \to 0 \frac{tan 3 x}{sin 2 x}

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\frac{3}{2}

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Solution

The correct option is B same as the value of $lim x \to 0 \frac{sin 2 x}{tan 3 x}$
The value of $lim x \to 0 \frac{\sqrt[3]{1 + sin x} - \sqrt[3]{1 - sin x}}{x}$
$lim x \to 0 \frac{(1 + sin x) - (1 - sin x)}{(1 + sin x)^{\frac{2}{3}} + (1 + sin x)^{\frac{1}{3}} (1 - sin x)^{\frac{1}{3}} + (1 - sin x)^{\frac{2}{3}}} . \frac{1}{x}$

$lim x \to 0 \frac{1}{(1 + sin x)^{\frac{2}{3}} + (1 + sin x)^{\frac{1}{3}} (1 - sin x)^{\frac{1}{3}} + (1 - sin x)^{\frac{2}{3}}} . \frac{2 sin x}{x}$
$= 2 \cdot 1 \cdot \frac{1}{3}$
$= \frac{2}{3}$
We can clearly observe from the given options that the value of $lim x \to 0 \frac{sin 2 x}{tan 3 x}$ is also $= \frac{2}{3}$

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Expansions to Remove Indeterminate Form

Standard XII Mathematics

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