InterviewSolution
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InterviewSolution
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Show that `lim_(xrarr2)(x)/([x])` does not exist. |
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Answer» Let `f(x)=(x)/({x}).` Then, `lim_(xto2^(+))f(x)=lim_(hto0)f(2+h)=lim_(hto0)(2+h)/([2+h])=1" "[becausehto0,[2+h]=2]` `lim_(xto2^(-))f(x)=lim_(hto0)f(2-h)=lim_(hto0)(2-h)/([2-h])=lim_(hto0)(2-h)/(1)=2" "[because[2-h]=1]` `thereforelim_(xto2^(+))f(x)nelim_(xto2^(-))f(x)and solim_(xto2)f(x)` does not exist. |
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