MCQs of Continuity and Differentiability

Showing 31 to 40 out of 130 Questions

31.

If we apply Rolle's theorem to f(x) = x³- 4x, x∈ [0, 2], then c = _____ .

32.

If x=secθ - cosθ, y=secⁿθ - cosⁿθ, then _____

33.

\frac{d}{d x} t a n^{- 1} \frac{\sqrt{1 + x^{2}} - \sqrt{1 - x^{2}}}{\sqrt{1 - x^{2}} + \sqrt{1 + x^{2}}} =_____|x| < 1

34.

\frac{d}{d x} (\frac{x}{2} \sqrt{a^{2} - x^{2}} + \frac{a^{2}}{2} s i n^{- 1} \frac{x}{a}) =_____(a > 0)

35.

Conditions of Mean Value Theorem are not applicable to_____in [- 1, 1] .

36.

For

f (x) = x + \frac{1}{x}, x \in [1, 3]

the value of c for mean-value theorem and for

f (x) = x^{2} - 4 x + 3

for Roll's theorem are _____ .

37.

If the tangent to the curve

y = x l o g x a t (c, f (x))

is parallel to the line-segment joining A(1, 0) and B(e, e), then c = _____ .

38.

If we apply the mean value theorem to

f (x) = 2 s i n x + s i n 2 x,

then c = _____ .

39.

If we apply the mean value theorem to

f (x) = \{\begin{array}{l} 2 + x^{3} x \leq 1 \\ 3 x x > 1 x \in [- 1, 2] \end{array}

then c = _____ .

40.

\frac{d}{d x} \frac{1}{\log |x|} =_____.

Showing 31 to 40 out of 130 Questions