MCQs of Continuity and Differentiability

Showing 81 to 90 out of 130 Questions

81.

If y = \sin^{- 1} (x \sqrt{1 - x} - \sqrt{x} \sqrt{1 - x^{2}}), then \frac{d y}{d x} =

_____

where (0 < x < 1)

82.

If f (x) = \cos^{- 1} [\frac{1 - {(\log x)}^{2}}{1 + {(\log x)}^{2}}], then f' (e) =

_____

83.

If for differential function f f (0) = 0, f (1) = 1, f' (0) = 4 = f' (1) and g (x) = f (e^{x}) \cdot e^{f (x)}, then g' (0) =

_____

84.

If x = f (t), y = g (t), then \frac{d^{2} y}{d x^{2}} =

85.

If y^{2} = {ax}^{2} + b, then \frac{d^{2} y}{d x^{2}} =

_____

86.

If y = \tan^{- 1} [\frac{{logex}^{- 2}}{{logex}^{2}}] + \tan^{- 1} [\frac{3 + 2 logx}{1 - 6 logx}], then \frac{d^{2} y}{d x^{2}} =

_____

w h e r e x > 1

87.

If x = \log t, y = t^{2} - 1, then at t = 1, y_{2} =

_____

88.

If x = \tan t, y = \tan p t, (1 + x^{2}) y_{2} + 2 k y_{1} = 0, then k =

_____

89.

If f is continuous at x = 0, then f (0) =

_____

w h e r e f (x) = \frac{{(27 - 2 x)}^{\frac{1}{3}} - 3}{9 - 3 {(243 + 5 x)}^{\frac{1}{5}}}, x \neq 0

90.

If {ax}^{2} + 2 hxy + {by}^{2} = 1, then \frac{d^{2} y}{{dx}^{2}} =

_____

Showing 81 to 90 out of 130 Questions