Lim x - 01-cos 2 x sin 5 x-x2sin 3 x-

The correct option is B 10/3 lim_x → 0(1 cos 2x) sin 5x/x^2 sin 3x = lim_x → 02 sin^2 x sin 5x/x^2 sin 3x = lim_x → 02 sin^2 x/x^2(sin 5x/5x ) × 5/(sin 3x/3x ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Sandwich Theorem

lim x → 01-co...

Question

${lim}_{x \to 0} \frac{(1 - c o s 2 x) s i n 5 x}{x^{2} s i n 3 x} =$

$\frac{10}{3}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$\frac{3}{10}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{6}{5}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{5}{6}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
$\frac{10}{3}$

${lim}_{x \to 0} \frac{(1 - c o s 2 x) s i n 5 x}{x^{2} s i n 3 x}$
$= {lim}_{x \to 0} \frac{2 s i n^{2} x s i n 5 x}{x^{2} s i n 3 x}$
$= {lim}_{x \to 0} \frac{\frac{2 s i n^{2} x}{x^{2}} (\frac{s i n 5 x}{5 x}) \times 5}{(\frac{s i n 3 x}{3 x}) 3}$
$= \frac{10 \times 1^{2} \times 1}{1 \times 3}$
$= \frac{10}{3}$

Suggest Corrections

Similar questions

Q. The value of

lim x \to 0 \frac{(1 - cos 2 x) sin 5 x}{x^{2} sin 3 x}

Q. The value of

lim x \to 0 \frac{(1 - cos 2 x) sin 5 x}{x^{2} sin 3 x}

equal to

lim x \to 0 \frac{(1 - cos 2 x) sin 5 x}{x^{2} sin 3 x}

lim x \to \infty \frac{(1 - cos 2 x) sin 5 x}{x^{2} sin 3 x}

is equal to

\lim_{x \to 0} \frac{1 - \cos 2 x}{3 \tan^{2} x}

Join BYJU'S Learning Program

limx→0(1−cos2x)sin5xx2sin3x=

The correct option is A 103 limx→0(1−cos2x)sin5xx2sin3x =limx→02sin2xsin5xx2sin3x =limx→02sin2xx2(sin5x5x)×5(sin3x3x)3 =10×12×11×3 =103

${lim}_{x \to 0} \frac{(1 - c o s 2 x) s i n 5 x}{x^{2} s i n 3 x} =$