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紧急求助lim(x→0)(ex-e-x)/sinx
题目详情
紧急求助lim(x→0)(ex-e-x)/sinx
▼优质解答
答案和解析
[e^x-e^(-x)]/sinx=[e^x-e^(-x)]/x*x/sinx
用洛必达法则求lim(x→0)[e^x-e^(-x)]/x=lim(x→0)[e^x+e^(-x)]=2
lim(x→0)[e^x-e^(-x)]/sinx=lim(x→0)[e^x-e^(-x)]/x*lim(x→0)x/sinx=2*1=2
用洛必达法则求lim(x→0)[e^x-e^(-x)]/x=lim(x→0)[e^x+e^(-x)]=2
lim(x→0)[e^x-e^(-x)]/sinx=lim(x→0)[e^x-e^(-x)]/x*lim(x→0)x/sinx=2*1=2
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