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Let f(x)={:{((3x)/(|x|+2x)',xne0),(0",",...

Let `f(x)={:{((3x)/(|x|+2x)',xne0),(0",",x=0.):}`
Show that `lim_(xrarr0)f(x)` does not exist.

Text Solution

Verified by Experts

The correct Answer is:
`k=1`
`lim_(xto2)f(x)=lim_(hto0)f(0+h)=lim_(hto0)cosh=1.`
`lim_(xto0^(-))f(x)=lim_(hto0)f(0-h)=lim_(hto0)f(-h)=lim_(hto0){(-h)+k}=k.`
Since `lim_(xto0)f(x)"exists, we have"lim_(xto0^(+))f(x)=lim_(xto0^(-))f(x)"and hance"k=1.`
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