Evaluate `lim_(xrarr(pi)/(4))((sinx-cosx))/((x-(pi)/(4))).`

Explanation

Put `(x-(pi)/(4))=y"so that when"y to (pi)/(4) then y to 0.`
`thereforelim_(xto(pi)/(4))((sinx-cosx))/((x-(pi)/(4)))`
`=lim_(yto0)({sin""((pi)/(4)+y)-cos((pi)/(4)+y)})/(y)" "["putting""("x-(pi)/(4)")"=y]`
`=lim_(yto0)({(sin""(pi)/(4)cosy+cos""(pi)/(4)siny)-(cos""(pi)/(4)cosy-sin""(pi)/(4)siny)})/(y)`
`=(2)/(sqrt2)xxlim_(yto0)((siny)/(y))=(2sqrtxx1)=sqrt2.`