Question

计算下列极限lim/x-0 e -x +e x -2/ 1-cosx

Answer 1

lim(x→0) (e^-x+e^x -2)/(1-cosx)

(x→0) e^-x+e^x-2 →0 1-cosx →0

lim(x→0)(e^-x+e^x-2)/(1-cosx)=lim(x→0) (e^x-e^-x)/sinx

x→0 e^x-e^-x →0 sinx→0

lim(x→0)(e^x-e^-x)/sinx=lim(x→0) (e^x+e^-x)/cosx=2

lim(x→0)(e^-x+e^x-2)/(1-cosx)=2