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If f(x)={{:(x","" "xlt0),(1","" "x=0),(x...

If `f(x)={{:(x","" "xlt0),(1","" "x=0),(x^(2)","" "xgt0):}," then find " lim_(xto0) f(x)"` if exists.

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The correct Answer is:
0
We have `underset(xto0^(-))limf(x)=underset(xto0)limx=0`
and `underset(xto0^(+))limf(x)=underset(xto0)limx^(2)=2`
Hence, `underset(xto0)limf(x)` is equal `" to "0.`
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