MCQs of Continuity and Differentiability

Showing 101 to 110 out of 130 Questions

101.

If y = a cosx - b sinx, then

y^{2} + (y_{1})^{2}

=_____ .

(a^{2} + b^{2} \neq 0)

102.

\frac{d}{d x} (x^{3} + \cos^{2} x)^{3}

=_____ .

103.

If f (x) = x^{n} then f (1) - \frac{f' (1)}{1!} + \frac{f'' (1)}{2!} - \frac{f''' (1)}{3!} + . . . + {(- 1)}^{n} \frac{f^{n} (1)}{n!} =

_____

104.

If f is differentiable at x = 1 and \lim_{h \to 0} \frac{f (1 + h)}{h} = 5, then f' (1) =

_____

105.

f (x) = \frac{x}{1 + |x|} is differentiable in

106.

If x^{a} y^{b} = {(x + y)}^{a + b}, then \frac{d y}{d x} =

_____

107.

f (x) = \{\begin{cases} (x - 1) \sin \frac{1}{x - 1} & ; x \neq 1 \\ 0 & ; x = 1 \end{cases} then which one of the following is true ?

(a)	f is not differentiable at x=0 and x=1
(b)	f is differentiable at x=0 and x=1
(c)	f is differentiable at x=0 and is not differentiable at x=1
(d)	f is differentiable at x=1 and is not differentiable at x=0

108.

If f is differentiable at x = a, then \lim_{x \to a} \frac{x^{2} f (a) - a^{2} f (x)}{x - a} =

_____

109.

\frac{d^{2} x}{d y^{2}} =

110.

If y = s e c (\tan^{- 1} x) then \frac{d y}{d x} a t x = 1 is equal to

_____

Showing 101 to 110 out of 130 Questions