The number of solutions of equation - -1x-1-1 -1 x-2 -1 is

The correct option is B 1 Let f(x) = π cot^ 1(x–1) + (π 1) cot^ 1 x f '(x) = π/(x 1)^2+1 (π 1)/x^2+1 lt; 0∀ x ϵ R Hence f(x) is decreasing function ...

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Standard XII

Mathematics

Exponential Function (a^x)

The number of...

Question

The number of solutions of equation $π c o t^{- 1} (x - 1) + (π - 1) c o t^{- 1} x = 2 π - 1$ is

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Solution

The correct option is B
1

Let $f (x) = π c o t^{- 1} (x - 1) + (π - 1) c o t^{- 1} x f^{'} (x) = - \frac{π}{(x - 1)^{2} + 1} - \frac{(π - 1)}{x^{2} + 1} < 0 \forall x ϵ R$
Hence f(x) is decreasing function
$∴ f (x) = 2 π - 1$ has only one solution

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The number of solutions of equation πcot−1(x−1)+(π−1)cot−1x=2π−1 is

The correct option is B 1 Let f(x)=πcot−1(x–1)+(π−1)cot−1xf′(x)=−π(x−1)2+1−(π−1)x2+1<0∀ xϵR Hence f(x) is decreasing function ∴f(x)=2π−1 has only one solution

The number of solutions of equation $π c o t^{- 1} (x - 1) + (π - 1) c o t^{- 1} x = 2 π - 1$ is

The correct option is B
1

Let $f (x) = π c o t^{- 1} (x - 1) + (π - 1) c o t^{- 1} x f^{'} (x) = - \frac{π}{(x - 1)^{2} + 1} - \frac{(π - 1)}{x^{2} + 1} < 0 \forall x ϵ R$
Hence f(x) is decreasing function
$∴ f (x) = 2 π - 1$ has only one solution