Show that the functions `f(x)` given by `f(x)={xsin1/x ,\ \ \ x!=0 0,\ \ \ \ \ \ \ \ \ \ \ \ \ \ x=0` is continuous at `x=0`

Explanation

`lim _{x rightarrow a} f(x)=f(a) `

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lim _{x rightarrow a^{+}} f(a+h)=lim _{x rightarrow a^{-}} f(a-h)=f(a)`

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lim _{x rightarrow 0} frac{sin x}{x}=1`

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(iii) lim _{x rightarrow a}{f(x) cdot g(x)}=1 cdot m,`


here `lim _{x rightarrow a} f(x)=1, lim _{x rightarrow a} g(x)=m`


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