Question

Which point is not a point of discontinuity of the function f(x) = $\left\{ \begin{matrix} \frac{\lbrack x\rbrack^{2} + \sin\lbrack x\rbrack}{\lbrack x\rbrack} & for\lbrack x\rbrack \neq 0 \\ 0 & for\lbrack x\rbrack = 0 \end{matrix} \right.\$

• A. x = 0
• B. x = $\lim_{x \rightarrow 0}$
• C. x = π
• D. x = $\lim_{h \rightarrow 0}$

Answer 1

Answer: (D)

x = $\lim_{h \rightarrow 0}$

Answer 2

f(x) is continuous except at the positive points where

1 – cos 4x = 0. Thus x = 0, x = $\frac { \pi } { 2 }$ and x = p are point of

discontinuity.

Hence x = $\frac { \pi } { 4 }$ is not a point of discontinuity.