Lim x - 0sin 3 x-sin 5 x-

The correct option is B 3/5We have,lim_x→ 0sin 3x/sin 5x This is an indeterminate limit of the form 0/0 Applying L'Hospital's Rule, lim_x → 0sin 3x/sin 5x = ...

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Standard XI

Mathematics

L'Hospital Rule to Remove Indeterminate Form

lim x → 0sin ...

Question

$lim x \to 0 \frac{s i n 3 x}{s i n 5 x} =$

-2

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\frac{3}{5}

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\frac{5}{3}

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Solution

The correct option is B $\frac{3}{5}$
We have, $lim x \to 0 \frac{s i n 3 x}{s i n 5 x}$
This is an indeterminate limit of the form $\frac{0}{0}$

Applying L'Hospital's Rule,

$lim x \to 0 \frac{s i n 3 x}{s i n 5 x} = lim x \to 0 \frac{c o s 3 x \frac{d}{d x} 3 x}{c o s 5 x \frac{d}{d x} 3 x}$

$= lim x \to 0 \frac{3 c o s 3 x}{5 c o s 5 x}$

Substituting x=0, the limit evaluates to $\frac{3}{5}$

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Similar questions

$lim x \to 0 \frac{sin 3 x}{sin 5 x}$ is equal to

\lim_{x \to 0} \frac{\sin 3 x - \sin x}{\sin x}

\lim_{x \to 0} \frac{\sin 3 x + 7 x}{4 x + \sin 2 x}

${lim}_{x \to 0} \frac{s i n 3 x + 7 x}{4 x + s i n 2 x}$

Q. Evaluate :

lim x \to 0 \frac{sin 3 x - s i n x}{sin x} .

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limx→0sin 3xsin 5x=

The correct option is B 35We have,limx→0sin 3xsin 5x This is an indeterminate limit of the form 00 Applying L'Hospital's Rule, limx→0sin 3xsin 5x=limx→0cos 3xddx 3xcos 5xddx3x =limx→03 cos 3x5 cos 5x Substituting x=0, the limit evaluates to 35

$lim x \to 0 \frac{s i n 3 x}{s i n 5 x} =$