Q64 of 107 Page 107

If y = tan^-1x, find in terms of y alone.

Given: y = tan^-1x …(i)

⇒ tan y = x

On differentiating Eq. (i) with respect to x, we get

Now, again differentiating the above with respect to x, we get

If x sin (a + y) + sin a cos (a + y) = 0, prove that

If prove that

Verify the Rolle’s theorem for each of the functions

f(x) = x (x – 1)² in [0, 1].

Verify the Rolle’s theorem for each of the functions

If y = tan-1x, find in terms of y alone.