Question

limx[ln(x+1)-lnx](x趋于正无穷)的值,求过程.

Answer 1

lim_{x趋于正无穷}(1+1/x)^x = e
lim_{x趋于正无穷}{x[ln(x+1)-lnx]}=lim_{x趋于正无穷}{xln[(x+1)/x]}
=lim_{x趋于正无穷}ln{[(x+1)/x]^x}
=lim_{x趋于正无穷}ln[(1+1/x)^x]
=ln(e)
=1