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

Let `f(x)={{:(4x-5",",xle2),(x-a",",xgt2.):}` If `lim_(xrarr2)f(x)` ex

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