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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
Question
Show that function $f(x)=x^2, x=0$ is continuous.
✓

Answer

Given function is defined at $x=0$ and the value of this is zero.$
\lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0} x^2=0
$
Thus $\quad \lim _{x \rightarrow 0} f(x)=f(x)=0=f(0)$
hence $f$ is continuous at $x=0$.

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