Question

求极限！！~~~~

lim x→0 sin2x/sin5xlim x→0 (1-cos2x)/x²lim x→0 in(1-x/2)^1/xlim x→∞ (1+2/x)^2x+1
lim x→0 sin2x/sin5x
lim x→0 (1-cos2x)/x²
lim x→0 in(1-x/2)^1/x
lim x→∞ (1+2/x)^2x+1

lim x→3 (x-3)cos1/(x-3)

lim x→0 (e^sinx-e^x)/(sinx-x)

Answer 1

lim x→0 sin2x/sin5x=lim x→0 2x/5x=2/5
lim x→0 (1-cos2x)/x²=lim x→0 [(4x²)/2]/x²=2
lim x→0 in(1-x/2)^1/x=e^(lim x→0(-x/2·1/x)=e^(-1/2)
lim x→∞ (1+2/x)^2x+1=e^(lim x→∞(2/x·(2x+1))=e^(4)

lim x→3 (x-3)cos1/(x-3)=0 (无穷小和有界函数乘积)lim x→0 (e^sinx-e^x)/(sinx-x)
=lim x→0e^x (e^(sinx-x)-1)/(sinx-x)
=lim x→0 e^x (sinx-x)/(sinx-x)
=e^0
=1

追问

亲爱的，详细解答好不好，我加分。求TAT

追答

够详细了啊。

就应该这样答。