Class 12

Continuity and Differentiation question bank (Maths)

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Q1.

If $f(x) = \begin{cases} x, & x \gt 1 \\ x^2, & x \lt 1 \end{cases}$,then $\lim_{x \to 1} f(x) =$

(A)

$x^2$

(B)

$x$

(C)

$-1$

(D)

$1$

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Q2.

Let the function $f$ be defined by the equation $f(x) = \begin{cases} 3x & \text{if } 0 \le x \le 1 \\ 5 - 3x & \text{if } 1 \lt x \le 2 \end{cases}$,then:

(A)

$\lim_{x \to 1} f(x) = f(1)$

(B)

$\lim_{x \to 1} f(x) = 3$

(C)

$\lim_{x \to 1} f(x) = 2$

(D)

$\lim_{x \to 1} f(x)$ does not exist

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