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Show that, lim(xto(pi//4)) (|x-4|)/(x-4)...

Show that, `lim_(xto(pi//4)) (|x-4|)/(x-4)`, does not exist,

Text Solution

Verified by Experts

Given, `underset(xto(pi//4))"lim"(|x-4|)/(x-4)`
LHL `=underset(xto(pi^(-4)//4))"lim"(-(x-4)/(x-4))` `[therefore|x-4|,xlt4]`
`=-1`
RHL`=underset(xto(x^(+)//4))"lim"(x-4)/(x-4)=1`
`therefore` LHL `ne` RHL
So, limit does not exist.
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