Lim x - 0 tan -1 x-sin -1 x-x3 is equal toA- -1B- 1 - 2C- -1 - 2D- 1

The correct option is C 1/2 x→ 0limtan^ 1x sin^ 1x/x^3 ( 0/0form ) x→ 0lim1/1+x^2 1/√(1 x^2)/3x^2 x→ 0lim√(1 x^2) (1+x^2)/3x^2(1+x^2)√(1 x^2) x→ 0lim(1 x^ ...

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Byju's Answer

Standard XII

Mathematics

L'Hospital Rule to Remove Indeterminate Form

lim x → 0 tan...

Question

${lim}_{x \to 0} \frac{t a n^{- 1} x - s i n^{- 1} x}{x^{3}} is equal to$

1/2

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-1/2

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-1

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Solution

The correct option is B
-1/2

$l i m x \to 0 \frac{t a n^{- 1} x - s i n^{- 1} x}{x^{3}} (\frac{0}{0} f o r m) l i m x \to 0 \frac{\frac{1}{1 + x^{2}} - \frac{1}{\sqrt{1 - x^{2}}}}{3 x^{2}} l i m x \to 0 \frac{\sqrt{1 - x^{2}} - (1 + x^{2})}{3 x^{2} (1 + x^{2}) \sqrt{1 - x^{2}}} l i m x \to 0 \frac{(1 - x^{2}) - (1 + x^{2})^{2}}{3 x^{2} (1 + x^{2}) \sqrt{1 - x^{2}} [\sqrt{1 - x^{2}} + (1 + x^{2})]} = - \frac{3}{6} = - \frac{1}{2}$

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Similar questions

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limx→0tan−1x−sin−1xx3is equal to

The correct option is B -1/2 limx→0tan−1x−sin−1xx3 (00form)limx→011+x2−1√1−x23x2limx→0√1−x2−(1+x2)3x2(1+x2)√1−x2limx→0(1−x2)−(1+x2)23x2(1+x2)√1−x2[√1−x2+(1+x2)]=−36=−12

${lim}_{x \to 0} \frac{t a n^{- 1} x - s i n^{- 1} x}{x^{3}} is equal to$