MCQs of Continuity and Differentiability

Showing 71 to 80 out of 130 Questions

71.

At how many point the function f (x) = |x - 0.5| + |x - 1| + \tan x is not differentiable (0, 2)

72.

If x^{2} + y^{2} = t + \frac{1}{t} and x^{4} + y^{4} = t^{2} + \frac{1}{t^{2}}, then \frac{d y}{d x} =

_____

73.

If y = \frac{1}{1 + x^{β - α} + x^{γ - α}} + \frac{1}{1 + x^{α - β} + x^{γ - β}} + \frac{1}{1 + x^{α - γ} + x^{β - γ}}, then \frac{d y}{d x} =

_____

74.

\frac{d}{d x} [\log \{e^{x} {(\frac{x - 2}{x + 2})}^{\frac{3}{4}}\}] =

_____

75.

If f (x) = \sqrt{x - 1} + \sqrt{x + 24 - 10 \sqrt{x - 1}}, 1 < x < 26 is real function, then f' (x)

= _____

76.

If f (x) = \log {}_{x^{2}}{(\log x)}, then f (e) =

_____

(x \in R^{+})

77.

If y = a^{x^{a^{x} . . . . . . . \infty}}, then \frac{d y}{d x} =

_____

78.

If f (x) = c o t^{- 1} (\frac{x^{x} - x^{- x}}{2}), then f' (1) =

_____

79.

If y = \tan^{- 1} (\frac{3 a^{2} x - x^{3}}{a (a^{2} - 3 x^{2})}), then \frac{d y}{d x} =

_____

where a, x > 0, 0 < \frac{x}{a} < \sqrt{3}

80.

If y = \sum_{r = 1}^{x} \tan^{- 1} \frac{1}{1 + r + r^{2}}, then \frac{d y}{d x} =

____

Showing 71 to 80 out of 130 Questions