((3x+1)/(3+x))^(1/(x-1)) 当x趋向于1时的极限

题目

((3x+1)/(3+x))^(1/(x-1)) 当x趋向于1时的极限

答案

设 f(x) = ((3x+1)/(3+x))^(1/(x-1)) ln f(x) = 1/(x-1) * ln[(3x+1) /(x+3) ] = 1/(x-1) * ln[ 1+ 2(x-1) /(x+3) ]当x->1 时,2(x-1) /(x+3) ->0,ln[ 1+ 2(x-1) /(x+3) ] 2(x-1) /(x+3) lim(x->1) lnf(x) = lim(x->1...