MCQs of Continuity and Differentiability

Showing 51 to 60 out of 130 Questions

51.

If y = \sqrt{1 + \cos 2 x}, \frac{3 π}{2} < x < 2 π, then \frac{d y}{d x} =

_____

52.

If y = \sqrt{1 - \sin 2 x}, \frac{π}{4} < x < \frac{π}{2}, then \frac{d y}{d x}

= _____

53.

If y = \tan^{- 1} (cotx) + \cot^{- 1} (tanx), 0 < x < \frac{π}{2}, then \frac{d y}{d x}

= _____

54.

f' (x) = f (x) a n d f (0) = 1, t h e n \lim_{x \to 0} \frac{f (x) - 1}{x} =

_____

55.

If y = 1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + . . . \infty, then \frac{d y}{d x} =

_____

56.

If y = \cos^{- 1} (x^{- 1}), then y' (- 2) =

______

57.

If f is defined for all x \in R and f is differentiable for all x \in R (x \neq 0) and f (x^{3}) = x^{5}, then f' (27) =

______

58.

If y = f (\sin x) and f' (x) = \sin^{- 1} x, then \frac{d y}{d x} =

_____

59.

If \sin^{- 1} x + \sin^{- 1} y = \frac{π}{2}, then \frac{d y}{d x}

= _____

60.

If f (x) = |x - 1| + |x - 3|, then f' (2) =

_____

Showing 51 to 60 out of 130 Questions