Lim x - 02 sin x-sin 2 x-x3 is equal to

The correct option is A x→ 0lim2sin x sin 2x/x^3 = x→ 0lim2 sin x(1 cos x)(1+cos x)/x^3(1+cos x) = x→ 0lim 2 sin^3x/x^3×1/1+cos x = 2 × (1)^3 ×1/1+1 = 1 ...

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

Byju's Answer

Standard XI

Mathematics

Standard Limits to Remove Indeterminate Form

lim x → 02 si...

Question

$lim x \to 0 \frac{2 sin x - sin 2 x}{x^{3}}$ is equal to

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

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

does not exist

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

Open in App

Solution

The correct option is A
$lim x \to 0 \frac{2 sin x - sin 2 x}{x^{3}}$
$= lim x \to 0 \frac{2 sin x (1 - cos x) (1 + cos x)}{x^{3} (1 + cos x)}$
$= lim x \to 0 2 \frac{{sin}^{3} x}{x^{3}} \times \frac{1}{1 + cos x}$
$= 2 \times (1)^{3} \times \frac{1}{1 + 1} = 1$

Suggest Corrections

Similar questions

\lim_{x \to 0} \frac{2 \sin x^{\circ} - \sin 2 x^{\circ}}{x^{3}}

${lim}_{x \to 0} \frac{2 s i n x - s i n 2 x}{x^{3}}$

lim x \to 0 \frac{(2^{sin x} - 1) (I n (1 + sin 2 x))}{x {tan}^{- 1} x}

equal:

Q. Prove that

{lim}_{x \to 0} \frac{2 sin x - sin 2 x}{x^{2}}

{lim}_{x \to 0} \frac{2 sin x - sin 2 x}{x^{3}}

is equal to :-

Join BYJU'S Learning Program

limx→02sinx−sin2xx3 is equal to

The correct option is A limx→02sinx−sin2xx3 =limx→02sinx(1−cosx)(1+cosx)x3(1+cosx) =limx→02sin3xx3×11+cosx =2×(1)3×11+1=1

$lim x \to 0 \frac{2 sin x - sin 2 x}{x^{3}}$ is equal to

The correct option is A
$lim x \to 0 \frac{2 sin x - sin 2 x}{x^{3}}$
$= lim x \to 0 \frac{2 sin x (1 - cos x) (1 + cos x)}{x^{3} (1 + cos x)}$
$= lim x \to 0 2 \frac{{sin}^{3} x}{x^{3}} \times \frac{1}{1 + cos x}$
$= 2 \times (1)^{3} \times \frac{1}{1 + 1} = 1$