If x - 0limasin x-sin 2x-tan 3x is finite then find the value of a

lim_x→ 0asin x sin 2x/tan^3x=lim_x→ 0asin x 2sin xcos x/tan^3x=lim_x→ 0sin x(a 2cos x)/tan^3x = lim_x→ 0sin x[a 2(1 x^2/2!+.....)]/tan^3x=lim_x→ 0sin ...

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

Byju's Answer

Standard XII

Mathematics

Continuity of a Function

If x → 0lim...

Question

If $lim x \to 0 \frac{a sin x - sin 2 x}{{tan}^{3} x}$ is finite then find the value of $a$

Open in App

Solution

$lim x \to 0 \frac{a sin x - sin 2 x}{{tan}^{3} x} = lim x \to 0 \frac{a sin x - 2 sin x cos x}{{tan}^{3} x} = lim x \to 0 \frac{sin x (a - 2 cos x)}{{tan}^{3} x}$
$= lim x \to 0 \frac{sin x [a - 2 (1 - \frac{x^{2}}{2!} + . . . . .)]}{{tan}^{3} x} = lim x \to 0 \frac{sin x [(a - 2) + x^{2} (1 + higher power of x)]}{{tan}^{3} x}$
Hence for given limit to exist $a - 2 = 0 \Rightarrow a = 2$ , and corresponding limit is $1$ .

Suggest Corrections

Similar questions

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

is finite, then

a =

Q. If

lim x \to 0 \frac{a sin x - b x + {c x}^{2} + x^{3}}{2 x^{2} log (1 + x) - 2 x^{3} + x^{4}} = I

and

I

is finite, then

Q. The value of

a

for which

\frac{sin 2 x + a sin x}{x^{3}}

tends to a finite limit as

x \to 0

If $tan (3 x + 30) = 1$ then find the value of $x$ .

Q. Find the value of

sin 2 x + cos 2 x

0 \leq x \leq \frac{π}{2}

{sin}^{2} x = a

and

{cos}^{2} x = b

Join BYJU'S Learning Program

If limx→0asinx−sin2xtan3x is finite then find the value of a

limx→0asinx−sin2xtan3x=limx→0asinx−2sinxcosxtan3x=limx→0sinx(a−2cosx)tan3x=limx→0sinx[a−2(1−x22!+.....)]tan3x=limx→0sinx[(a−2)+x2(1+higher power of x)]tan3xHence for given limit to exist a−2=0⇒a=2, and corresponding limit is 1.

If $lim x \to 0 \frac{a sin x - sin 2 x}{{tan}^{3} x}$ is finite then find the value of $a$