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Let f(x)={{:(1+x^(2)",",0lexle1),(2-x","...

Let `f(x)={{:(1+x^(2)",",0lexle1),(2-x",",xgt1.):}`
Show that `lim_(xrarr0)f(x)` does not exist.

Text Solution

Verified by Experts

`lim_(xto1^(+))f(x)=lim_(hto0)f(1+h)=lim_(hto0){2-(1+h)}=lim_(hto0)(1-h)=1`
`lim_(3to1^(-))f(x)=lim_(hto0)f(1-h)=lim_(hto0){1+(1-h)^(2)}=lim_(hto0)(1+1+h^(2)-2h)=2.`
`thereforelim_(xto1^(+))f(x)nelim_(xto1^(-))f(x)andso limf(x)` does not exist.
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