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Show that lim(xrarr0)1/x does not exist....

Show that `lim_(xrarr0)1/x` does not exist.

Text Solution

Verified by Experts

The correct Answer is:
`k=6`
Let `f(x)=1/x,Then, lim_(xto0^(+))f(x)lim_(hto0)f(0+h)=lim_(xto0)f(h)=lim_(hto0)1/h=oo.`
`And, lim_(xto0^(-))f(x)=lim_(hto0)f(0-h)=lim_(hto0)f(-h)=lim_(hto0)(1)/(-h)=-oo.`
`thereforelim_(xto0^(+))f(x)nelim_(hto0)f(x)"and hance"lim_(xto0)f(x)` does not exist.
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