MCQs of Continuity and Differentiability

Showing 111 to 120 out of 130 Questions

111.

For a > 0, t \in (0, \frac{π}{2}) let x = \sqrt{a^{\sin^{- 1} t}} and y = \sqrt{a^{\cos^{- 1} t}} . Then 1 + {(\frac{d y}{d x})}^{2} equals .

112.

If the Rolle' s theorem holds for the function f (x) = 2 x^{3} + a x^{2} + b x in the interval [- 1, 1] for the point c = \frac{1}{2} then the value of 2 a + b :

113.

If the function f (x) = \{\begin{cases} \frac{\sqrt{2 + cosx} - 1}{{(π - x)}^{2}} & ; x \neq π \\ k & ; x = π \end{cases} is continuous at x = π then k is equals :

114.

If x = a (cost + \log \tan \frac{t}{2}), y = asint then \frac{d^{2} y}{{dx}^{2}} =

_____

115.

If y = e^{m \cos^{- 1} x} then m =

_____

116.

\frac{d}{d x} \sqrt{x \cos x}

=_____ .0<x<

\frac{π}{2}

117.

\frac{d}{d x} \tan^{- 1} \sqrt{\frac{1 - \sin x}{1 + \sin x}}

=_____ .-

\frac{3 π}{2}

<x<

\frac{3 π}{2}

118.

x = e^{\tan^{- 1} (\begin{matrix} y - x^{3} \\ x^{3} \end{matrix})}

, then

\frac{d y}{d x}

=_____ .

119.

\frac{d}{d x} [\sin^{- 1} (\frac{5 x}{13} + \frac{12}{13} \sqrt{1 - x^{2}})]

=_____ .(0<x<

\frac{π}{2}

)

120.

f (x) = \log_{3} (\log_{5} x)

, then f'(x)=_____ .

Showing 111 to 120 out of 130 Questions