Question

高数求极限题目x->0 lim{[2+e^(1/x)]/(1+e^(4/x)} + sinx/|x|

Answer 1

左极限是 lim

{[2+e^(1/x)]/[1+e^(4/x)]}-sinx/x

= (2+0)/(1+0)-1 = 1;

右极限是 lim

{[2+e^(1/x)]/[1+e^(4/x)]}+sinx/x

= lim

{[2e^(-4/x)+e^(-3/x)]/[e^(-4/x)+1]}+sinx/x

= (0+0)/(0+1)+1 = 1.

故所求极限是 1.