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Find (lim)(x->5)f(x), where f(x)=|x|-5...

Find `(lim)_(x->5)f(x)`, where `f(x)=|x|-5`

Text Solution

Verified by Experts

`f(x)=|x|-5`
at x=5
`LHL=underset(Xrarr5^(-)"lim"f(x)`
`=underset(hrarr0)"lim"f(5-h)`
`=underset(hrarr0)"lim"|5-h|-5`
`=5-5=0`
`RHL=underset(xrarr5^(+))"lim"f(x)`
`=underset(hrarr0)"lim"f(5+h)`
`=underset(hrarr0)"lim"|5+h|-5`
`=5-5=0`
`because LHL=RHL`
`therefore underset(Xrarr5)f(x)=0`
Let 5-h=x
`rARr 5-hrarr5`
`rArr hrarr0`
Let `5+h=x`
`rArr 5+hrarr 5`
`rArr hrarr0`
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