MCQs of Continuity and Differentiability

Showing 91 to 100 out of 130 Questions

91.

f : R \to R defined as f (x) = m a x \{x, x^{3}\} . The set of points at which f (x) is not differential is . . .

92.

If F (x) = {(f {(\frac{x}{2})}^{2} + g {(\frac{x}{2})}^{2})}^{2} where f'' (x) = - f (x), g (x) = f' (x) and F (5) = 5, then F (10) =

______

93.

y = ||x| - 1| is differentiable for values of x except

94.

If f (x) = 4 and f' (x) = 4 then \lim_{x \to 2} \frac{x f (2) - 2 f (x)}{x - 2} =

_____

95.

If f (1) = 1, f' (1) = 2 then \lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1} =

_____

96.

If f (x + y) = f (x) f (y), \forall x, y and f (5) = 2, f' (0) = 3 then f' (5) =

_____

97.

\lim_{x \to 0} \frac{\log (3 + x) - \log (3 - x)}{x} = k, then k =

_____

98.

f (x) = \{\begin{matrix} a x + b, 2 \leq x < 7 \\ 3 x - 2, 7 \leq x < 10 \\ b x - 11 a, x \geq 10 \end{matrix}

is continuous, then

99.

f (x) = \{\begin{cases} 2 x, x \in (0, 2) \\ 4, x \geq 2 \end{cases}

100.

\frac{d}{d x} \frac{2}{\log |x|}

= _____ .

Showing 91 to 100 out of 130 Questions