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Question Number 30366 by diyatrivedi last updated on 21/Feb/18

Commented by abdo imad last updated on 21/Feb/18

for x≠a ∣sin((1/(x−a)))∣≤1 ⇒∣x−a∣∣sin((1/(x−a)))∣≤∣x−a∣ but lim_(x→a) ∣x−a∣=0 ⇒ lim_(x→a) f(x)=0 =f(0) so f is continue at point x_0 =a .

forx≠a∣sin(1x−a)∣⩽1⇒∣x−a∣∣sin(1x−a)∣⩽∣x−a∣butlimx→a∣x−a∣=0⇒limx→af(x)=0=f(0)sofiscontinueatpointx0=a.

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