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Let f(x)={{:(4x-5",",xle2),(x-a",",xgt2....

Let `f(x)={{:(4x-5",",xle2),(x-a",",xgt2.):}`
If `lim_(xrarr2)f(x)` exists then find the value of a.

Text Solution

Verified by Experts

The correct Answer is:
`a=-1`
`lim_(xto2^(-))f(x)=lim_(hto0)f(2+h)=lim_(hto0)(2+h-a)=(2-a).`
`lim_(xto2^(-))f(x)=lim_(hto0)f(2-h)=lim_(hto0){4(2-h)-5}=(8-5)=3.`
Since `lim_(xto2^(-))f(x)` exist, we must have `lim_(xto2^(+))f(x)=lim_(xto2^(-))f(x).`
`therefore2-a=3impliesa=(2-3)=-1.`
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