lim【e^2x-e^(-x)】/[3e^x+2e^2x]求x趋于正无穷的极限

lim【e^2x-e^(-x)】/[3e^x+2e^2x]求x趋于正无穷的极限
lim【e^2x-e^(-x)】/[3e^x+2e^2x]求x趋于正无穷的极限

lim【e^2x-e^(-x)】/[3e^x+2e^2x]求x趋于正无穷的极限
上下除以e^2x
原式=lim【1-e^(-3x)】/[3e^(-x)+2]
e^(-x)趋于0
所以原式=1/2

lim(x->无穷)【e^2x-e^(-x)】/[3e^x+2e^2x]
=lim(x->无穷) [ 1- e^(-3x)]/[3e^(-x)+2]
=1/2