Question

lim(x→∞)(x²+1)/(x-1)=? lim(x→∞)(e^n + e^-n)/(e^n - e^-n)=? lim(x→0)tan7x/sin5x=? 帮我求下

Answer 1

lim(x→∞)(x²+1)/(x-1)
=lim(x→∞)(x+1/x)/(1-1/x)
=lim(x→∞)x
=∞
lim(n→∞)(e^n + e^-n)/(e^n - e^-n)
=lim(n→∞)e^n/e^n
=1
lim(x→0)tan7x/sin5x
=lim(x→0)sin7x/sin5xcos7x
=lim(x→0)7x/5xcos7x
=7/5

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追问

好奇怪，第一题结果怎么是无穷啊

追答

分子x^2是分母x的高阶无穷大
结果是无穷大