lim x->inf (e^(2x)/sinh(2x))=?
回答 (2)
2018-11-20 7:08 am
Remember: sinh(t) = (1/2) * (e^(t) - e^(-t))
e^(2x) / sinh(2x) =>
e^(2x) / ((1/2) * (e^(2x) - e^(-2x))) =>
2 * e^(2x) / (e^(2x) - e^(-2x)) =>
2 * e^(2x) / (e^(2x) * (1 - e^(-4x))) =>
2 / (1 - e^(-4x))
x goes to infinity
2 / (1 - e^(-4 * inf)) =>
2 / (1 - e^(-inf)) =>
2 / (1 - 0) =>
2 / 1 =>
2
e^(2x) / sinh(2x) =>
e^(2x) / ((1/2) * (e^(2x) - e^(-2x))) =>
2 * e^(2x) / (e^(2x) - e^(-2x)) =>
2 * e^(2x) / (e^(2x) * (1 - e^(-4x))) =>
2 / (1 - e^(-4x))
x goes to infinity
2 / (1 - e^(-4 * inf)) =>
2 / (1 - e^(-inf)) =>
2 / (1 - 0) =>
2 / 1 =>
2
2018-11-20 7:47 am
sinh(2x)=½(-e⁻²ˣ+e²ˣ)
lim (e²ˣ)/½(-e⁻²ˣ+e²ˣ)=2(e²ˣ)/(e²ˣ)=2❌1=2
x→∞
lim (e²ˣ)/½(-e⁻²ˣ+e²ˣ)=2(e²ˣ)/(e²ˣ)=2❌1=2
x→∞
收錄日期: 2021-04-24 01:10:58
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https://hk.answers.yahoo.com/question/index?qid=20181119230122AAOTXFN