The value oflimx-0-1-sinx-1-sinx-xis

Lim_x→0√(1+sinx) √(1 sinx)/x =lim_x→0(1+sinx) (1 sin s)/(1+sin x)^2/3+(1+sin x)^2/3+(1 sin x)^2/3(1 sinx)^2/3×1/x =lim_x→02/(1+sin x)^2/3+(1+sin x)^1/3+(1 sin ...

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Byju's Answer

Standard XIII

Mathematics

Rationalization Method to Remove Indeterminate Form

The value ofl...

Question

$The value of {lim}_{x \to 0} \frac{\sqrt[3]{1 + s i n x} - \sqrt[3]{1 - s i n x}}{x} i s$

2/3

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-2/3

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3/2

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-3/2

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Solution

The correct option is A
2/3

${lim}_{x \to 0} \frac{\sqrt[3]{1 + s i n x} - \sqrt[3]{1 - s i n x}}{x} = {lim}_{x \to 0} \frac{(1 + s i n x) - (1 - s i n s)}{(1 + s i n x)^{2 / 3} + (1 + s i n x)^{2 / 3} + (1 - s i n x)^{2 / 3} (1 - s i n x)^{2 / 3}} \times \frac{1}{x} = {lim}_{x \to 0} \frac{2}{(1 + s i n x)^{2 / 3} + (1 + s i n x)^{1 / 3} + (1 - s i n x)^{1 / 3} + (1 - s i n x)^{2 / 3}} \times \frac{s i n (x)}{x}$
= $\frac{2}{3} .1 = \frac{2}{3}$

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Similar questions

{lim}_{x \to 0} \frac{\sqrt[3]{1 + s i n x} - \sqrt[3]{1 - s i n x}}{x}

Q. Calculate the following limits.

lim x \to 0 \frac{\sqrt[3]{1 + sin x} - \sqrt[3]{1 - sin x}}{x} .

Q. If

s i n (x - y) = \frac{1}{2}

s i n (x + y) = \frac{\sqrt 3}{2}

, and

0 < y < x < 90^{\circ}

, find the value of x and y, respectively.

{cot}^{- 1} (\frac{\sqrt{1 - sin x} + \sqrt{1 + sin x}}{\sqrt{1 - sin x} - \sqrt{1 + sin x}})

=....

(0 < x < \frac{π}{2})

lim x \to \frac{n}{2} \frac{1 - (sin x)^{\frac{- 1}{3}}}{1 - (sin x)^{\frac{- 2}{3}}}

is?

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The value oflimx→03√1+sinx−3√1−sinxxis

The correct option is A 2/3 limx→03√1+sinx−3√1−sinxx=limx→0(1+sinx)−(1−sin s)(1+sin x)2/3+(1+sin x)2/3+(1−sin x)2/3(1−sinx)2/3×1x=limx→02(1+sin x)2/3+(1+sin x)1/3+(1−sin x)1/3+(1−sinx)2/3×sin(x)x = 23.1=23

$The value of {lim}_{x \to 0} \frac{\sqrt[3]{1 + s i n x} - \sqrt[3]{1 - s i n x}}{x} i s$