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`f(x)=sgn(x)={{:(1", "xgt0),(-1", "xlt0),(0", "x=0):}` <br> `:." "underset(xto0^(+))limf(x)=1" and "underset(xto0^(+))limf(x)=-1` <br> Now `f(x)xxg(x)={{:(x^(3)", "xgt0),(-x^(3)", "xlt0),(0", "x=0):}` <br> `:." "underset(xto0^(+))limf(x).g(x)=underset(xto0^(+))limx^(3)=0` <br> and`" "underset(xto0^(-))limf(x).g(x)=underset(xto0^(+))lim(-x^(3))=0` <br> Thus`" "underset(xto0)limf(x).g(x)` exists.**Revision of limits**

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