Discuss the continuity of `f(x)={x^2sin(1/x),\ \ \ \ x!=0\ \ \ \ \ \ \ \ \ \ \ 0,\ \ \ \ \ \ \ \ \ \ x=0` at `x=0`

Explanation

`f(x)=
x^{2} sin frac{1}{x}, x ne 0 `
`
0, x=0`


We see


`lim _{x rightarrow 0} x^{2} sin (frac{1}{x})=lim _{x rightarrow 0} x^{2} lim _{x rightarrow 0} sin (frac{1}{x})=0 times lim _{x rightarrow 0} sin (frac{1}{x})=0 `

`Rightarrow lim _{x rightarrow 0} f(x)=f(0)`

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