MCQs of Continuity and Differentiability

Showing 111 to 117 out of 117 Questions

111.

x = \frac{t}{1 + t}

and

y = \frac{1 - t}{1 + t}

, then

\frac{d y}{d x}

=_____ .

112.

\frac{d}{d x} e^{x \log (x - 1)}

=_____ .

113.

x = 2 b t

y = b t^{2}

, then

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

=_____ .

114.

\frac{d}{d x} [\frac{x}{2} \sqrt{x^{2} - a^{2}} - \frac{a^{2}}{2} \log |x + \sqrt{x^{2} - a^{2}}|]

=______ .x>a>0

115.

Condition of Rolle's theorem are not applicable to _____ in [-2,2].

116.

f (x) = |\begin{matrix} x^{2} & x^{3} & 3 x^{2} \\ 1 & - 6 & 4 \\ p & p^{2} & p^{3} \end{matrix}|,

where p is constant then

\frac{d^{2}}{d x^{2}} (f (x))

=_____ .

(a)	is directly proportional to x²
(b)	is directly proportional to x
(c)	is directly proportional to x³
(d)	is constant

117.

\frac{d}{d x} [\sqrt{\sin x^{3}}]

=_____

Showing 111 to 117 out of 117 Questions