InterviewSolution
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InterviewSolution
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Show that `("lim")_(x->0)x/(|x|)`does not exist. |
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Answer» Let `f(x)=(x)/(|x|).` Then, `underset(xto0^(+))limf(x)=underset(hto0)limf(0+h)=underset(hto0)limf(h)=underset(hto0)lim(h)/(|h|)=underset(hto0)limh/h=1.` `underset(xto0^(-))limf(x)underset (xto0)limf(0-h)=underset(hto0)limf(-h)=underset(hto0)lim(-h)/(|-h|)=underset(hto0)lim(-h)/(h)=-1.` `thereforeunderset(xto0^(+))limf(x)neunderset(xto0^(-))limf(x).` Hence, `underset(xto0)limf(x)` does not exist. |
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