Class 12

Continuity and Differentiation question bank (Maths)

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Q1.

If $f(x) = |x - 2|$,then

(A)

$\mathop {\lim }\limits_{x \to 2^+} f(x) \ne 0$

(B)

$\mathop {\lim }\limits_{x \to 2^-} f(x) \ne 0$

(C)

$\mathop {\lim }\limits_{x \to 2^+} f(x) \ne \mathop {\lim }\limits_{x \to 2^-} f(x)$

(D)

$f(x)$ is continuous at $x = 2$

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Q2.

Let $f(x) = \begin{cases} x^2 + k, & \text{when } x \ge 0 \\ -x^2 - k, & \text{when } x \lt 0 \end{cases}$. If the function $f(x)$ is continuous at $x = 0$,then $k =$

(A)

$0$

(B)

$1$

(C)

$2$

(D)

$-2$

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