作业帮x趋向正无穷 lim[(x+a)/(x-a)]^x利用x趋向正无穷 lim(1+1/x)^x=e
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/07 03:03:12
![x趋向正无穷 lim[(x+a)/(x-a)]^x利用x趋向正无穷 lim(1+1/x)^x=e](/uploads/image/z/1615646-38-6.jpg?t=x%E8%B6%8B%E5%90%91%E6%AD%A3%E6%97%A0%E7%A9%B7+lim%5B%28x%2Ba%29%2F%28x-a%29%5D%5Ex%E5%88%A9%E7%94%A8x%E8%B6%8B%E5%90%91%E6%AD%A3%E6%97%A0%E7%A9%B7+lim%281%2B1%2Fx%29%5Ex%3De)
x趋向正无穷 lim[(x+a)/(x-a)]^x利用x趋向正无穷 lim(1+1/x)^x=e
x趋向正无穷 lim[(x+a)/(x-a)]^x
利用x趋向正无穷 lim(1+1/x)^x=e
x趋向正无穷 lim[(x+a)/(x-a)]^x利用x趋向正无穷 lim(1+1/x)^x=e
lim[(x+a)/(x-a)]^x
=lim[1+2a/(x-a)]^{[(x-a)/2a]*[2ax/(x-a)]}
=e^lim[2ax/(x-a)]=e^(2a)