MHT-CET

Continuity and Differentiation question bank (Mathematics)

Practice 511 free MHT-CET Mathematics - Continuity and Differentiation questions with answers and step-by-step solutions.

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Q1.

At the point $x=1$,the function $f(x) = \begin{cases} x^3-1, & 1 \lt x \lt \infty \\ x-1, & -\infty \lt x \leq 1 \end{cases}$ is

(A)

continuous and differentiable

(B)

continuous and not differentiable

(C)

discontinuous and differentiable

(D)

discontinuous and not differentiable

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Q2.

The first derivative of the function $f(x) = \cos^{-1}\left(\sin \sqrt{\frac{1+x}{2}}\right) + x^x$ with respect to $x$ at $x=1$ is

(A)

$\frac{1}{4}$

(B)

$\frac{5}{4}$

(C)

$\frac{-1}{2}$

(D)

$\frac{3}{4}$

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