MCQs of Continuity and Differentiability

Showing 121 to 120 out of 130 Questions

121.

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

and

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

, then

\frac{d y}{d x}

=_____ .

122.

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

=_____ .

123.

x = 2 b t

y = b t^{2}

, then

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

=_____ .

124.

For the curve

f (x) = (x - 5)^{2}

applying mean value theorem on [3,7], the tangent at _____ is parallel to the chord joining A(3,4) and B(7,4).

125.

The value of c for the mean value theorem for f(x)=x³ in [-2,2] is _____ .

126.

If we apply the Rolle's theorem to f(x)=e^xcosx,

x \in [\frac{π}{2}, \frac{3 π}{2}]

,then c=_____ .

127.

\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

128.

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

129.

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

130.

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

=_____

Showing 121 to 120 out of 130 Questions