MCQs of Continuity and Differentiability

Showing 61 to 70 out of 130 Questions

61.

y = \tan^{- 1} (\frac{3 - 2 x}{2 + 3 x}), x > 0, then \frac{d y}{d x} =

_____

62.

{[\frac{d}{d x} \cot^{- 1} x]}_{x = - 2}

= _____ .

63.

\frac{d}{d x} x^{x - 1} =_____(x > 0)

64.

\frac{d}{d x} \log |x^{3}| =_____. (x \neq 0)

65.

for

f (x) = \{\begin{matrix} \frac{x^{3}}{a^{2}} - a, x < a \\ 0, x = a \\ a - \frac{x^{3}}{a^{2}}, x > a \end{matrix}

,_____ .

66.

If f (x) = c {os}^{- 1} x, then . \lim_{x \to 0.5} \frac{f (x) - f (0.5)}{x - 0.5}

67.

If f (x) = 2^{x} + 2^{x + 1} + 2^{x + 2} + . . . . + 2^{x + 9}, then f' (2) =

_____

68.

If g is inverse of f and f' (x) = \frac{1}{1 + x^{n}}, then g' (x) =

_____

69.

f (x) = \{\begin{cases} a x^{2} + b, b \neq 0; x \leq 1 \\ b x^{2} + a x + c; x > 1 \end{cases} If f is continuous and differentiable at x = 1, then

70.

f (x) = \frac{\sin [x]}{[x]}, [x] \neq 0 = k, [x] = 0 If f is continuous at x = 0, then k =

_____

Showing 61 to 70 out of 130 Questions