First slide

Continuity

Question

The function defined by $f (x) = \{\begin{cases} \begin{matrix} x . \sin \frac{1}{x} & f o r x \neq 0 \end{matrix} \\ \begin{matrix} 0 & , f o r x = 0 \end{matrix} \end{cases} a t x = 0 i s$

Moderate

A

continuous
B

only right continuous
C

only left continuous
D

can not be determined

Solution

LHL=RHL at x=0
$\lim_{x \to 0} x \sin \frac{1}{x} = 0 f (0) = 0$
f(x) is continuous at x = 0

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