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

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

Discussion