Class 12

Continuity and Differentiation question bank (Maths)

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Q1.

The function $f(x) = \frac{\log(1 + ax) - \log(1 - bx)}{x}$ is not defined at $x = 0$. The value which should be assigned to $f$ at $x = 0$ so that it is continuous at $x = 0$ is:

(A)

$a - b$

(B)

$a + b$

(C)

$\log a + \log b$

(D)

$\log a - \log b$

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Q2.

Let $f(x) = \begin{cases} x^p \sin \frac{1}{x}, & x \ne 0 \\ 0, & x = 0 \end{cases}$. Then $f(x)$ is continuous but not differentiable at $x = 0$ if:

(A)

$0 \lt p \le 1$

(B)

$1 \le p \lt \infty$

(C)

$-\infty \lt p \lt 0$

(D)

$p = 0$

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