x趋近于无穷时(x-1)^2/(x+1)的极限

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/27 17:49:00
x趋近于无穷时(x-1)^2/(x+1)的极限x趋近于无穷时(x-1)^2/(x+1)的极限x趋近于无穷时(x-1)^2/(x+1)的极限[(x-1)/(x+1)]^(x+2)=[1-2/(x+1)]

x趋近于无穷时(x-1)^2/(x+1)的极限
x趋近于无穷时(x-1)^2/(x+1)的极限

x趋近于无穷时(x-1)^2/(x+1)的极限

[(x-1)/(x+1)]^(x+2) = [1 - 2/(x+1)]^(x+2)
let t=(x+1)/2
[(x-1)/(x+1)]^(x+2) = [1 - 1/t]^(2t+1) = [(1 - 1/t)^t]^2 * (1 - 1/t)
lim (1 - 1/t)^t = 1/e
lim (1 - 1/t) = 1
lim [(x-1)/(x+1)]^(x+2) = 1/e²

无穷