MCQs of Continuity and Differentiability

Showing 21 to 30 out of 130 Questions

21.

\frac{d}{d x} x |x| =_____. (x < 0)

22.

If x = \frac{2 t}{1 + t^{2}}, y = \frac{1 - t^{2}}{1 + t^{2}}, then \frac{d y}{d x} =_____.

23.

\frac{d}{d x} e^{x l o g x} =_____

24.

\frac{d}{d x} \frac{t a n^{- 1} x}{1 + t a n^{- 1} x} w . r . t . t a n^{- 1} x =_____

25.

If x = a t^{2}, y = 2 a t, then \frac{d^{2} y}{d x^{2}}

26.

\frac{d}{d x} c o t^{- 1} \frac{\sqrt{1 + x^{2}} - 1}{x} =_____(x \in R - {0})

27.

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

28.

For the curve f(x) = (x - 3)² , applying mean value theorem on [2, 4] the tangent at _____ is parallel to the chord joining A(2, 1) and B(4, 1).

29.

The value of c for the mean-value theorem for f(x) = x³ in [-1 , 1] is _____ .

30.

If we apply the Rolle's theorem to f(x) = e^xsinx x∈ [0, π], then c = ______ .

Showing 21 to 30 out of 130 Questions