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Evaluate lim(x->0)(3x+|x|)/(7x-5|x|)...

Evaluate `lim_(x->0)(3x+|x|)/(7x-5|x|)`

Text Solution

Verified by Experts

The correct Answer is:
Limit does not exist.
`underset(xto0^(-))lim(3x+|x|)/(7x-5|x|)=underset(xto0^(-))lim(3x-x)/(7x-5x)=1/6`
and `underset(xto0^(+))lim(3x+|x|)/(7x-5|x|)=underset(xto0)lim(3x+x)/(7x-5x)=2`
Hence, the limit does not exist.
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