Question

lim x--->无穷[(x+c)/(x -c)]^x =lim x--->无穷[1+2c/(x -

lim x--->无穷[(x+c)/(x -c)]^x =lim x--->无穷[1+2c/(x -c )]^x =e^(2c) 请问这个答案是怎么得来的，请给出详细解答，谢谢

Answer 1

简单分析一下，答案如图所示

Answer 2

lim(x→∞) [(x + c)/(x - c)]^x
= lim(x→∞) [((x - c) + 2c)/(x - c)]^x
= lim(x→∞) [1 + 2c/(x - c)]^x
= {lim(x→∞) [1 + 1/((x - c)/(2c))]^(x - c)/(2c)} ^ lim(x→∞)[(2c)/(x - c) * x]
令t = (x - c)/(2c)，x→∞时t→∞
= {lim(t→∞) (1 + 1/t)^t} ^ 2c*lim(x→∞) x/(x - c)
= e^ 2c*lim(x→∞) 1/(1 - c/x)
= e^ 2c*1
= e^(2c)

Answer 3

buxiaode