Let f ( x ) = cot − 1 ( 1 − x 2 2 x ) and g ( x ) = cos − 1 ( 1 + x 2 1 − x 2 ) . For 0 < t < 1 , find lim x → t g ( x ) − g ( t ) f ( x ) − f ( t ) .

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MathematicsLimitsTrigonometric and Inverse Trigonometric limitsMedium2 minQB

MathematicsMediumsingle choice

Let $f (x) = cot^{- 1} (\frac{2 x}{1 - x ^{2}})$ and $g (x) = cos^{- 1} (\frac{1 - x ^{2}}{1 + x ^{2}})$ . For $0 < t < 1$ , find $lim_{x \to t} \frac{f ( x ) - f ( t )}{g ( x ) - g ( t )}$ .

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Answer:

Solution:

For $0 < x < 1, f (x) = π /2 - 2 tan^{- 1} x$ and $g (x) = 2 tan^{- 1} x$ . Therefore the required ratio is -1.

Stream:JEESubject:MathematicsTopic:LimitsSubtopic:Trigonometric and Inverse Trigonometric limits

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