X- 0Lt2x-sin -1x-2x-tan -1x- 1-a- Find a

x→ 0Lt2x sin ^ 1x/2x+tan ^ 1x = x→ 0Lt2x ( x+x^36+.... )2x+ ( x x^33⋯ nbsp; )= nbsp; Lt_x→ 0x x^36⋯3x x^33⋯ = x→ 0Lt1 x^26+⋯3 x^23+⋯= 13. ...

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Standard XII

Mathematics

Definition of Limit

x→ 0Lt2x-sin ...

Question

$L t x \to 0 \frac{2 x - {sin}^{- 1} x}{2 x + {tan}^{- 1} x} = \frac{1}{a} .$ Find $a$

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Solution

$L t x \to 0 \frac{2 x - {sin}^{- 1} x}{2 x + {tan}^{- 1} x}$
$= L t x \to 0 \frac{2 x - (x + \frac{x^{3}}{6} + . . . .)}{2 x + (x - \frac{x^{3}}{3} \dots)} = L t_{x \to 0} \frac{x - \frac{x^{3}}{6} \dots}{3 x - \frac{x^{3}}{3} \dots}$
$= L t x \to 0 \frac{1 - \frac{x^{2}}{6} + \dots}{3 - \frac{x^{2}}{3} + \dots} = \frac{1}{3} .$
$\Rightarrow a = 3$

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Ltx→02x−sin−1x2x+tan−1x=1a. Find a

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$L t x \to 0 \frac{2 x - {sin}^{- 1} x}{2 x + {tan}^{- 1} x} = \frac{1}{a} .$ Find $a$