4,5题用第一重要极限求
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解决时间 2021-02-15 21:53
- 提问者网友:原来太熟悉了会陌生
- 2021-02-15 18:19
4,5题用第一重要极限求
最佳答案
- 二级知识专家网友:迷人又混蛋
- 2021-02-15 18:43
(4)
lim (1-cos²x)/x²
x→0+
=lim sin²x/x²
x→0+
=lim (sinx/x)²
x→0+
=1²
=1
(5)
令4/x³=t,x→∞,则t→0
lim x³tan(4/x³)
x→∞
=lim 4tan(4/x³)/(4/x³)
x→∞
=lim 4tant/t
t→0
=lim 4(sint/cost)/t
t→0
=lim 4(sint/t)/cost
t→0
=4·1/cos0
=4/1
=4
lim (1-cos²x)/x²
x→0+
=lim sin²x/x²
x→0+
=lim (sinx/x)²
x→0+
=1²
=1
(5)
令4/x³=t,x→∞,则t→0
lim x³tan(4/x³)
x→∞
=lim 4tan(4/x³)/(4/x³)
x→∞
=lim 4tant/t
t→0
=lim 4(sint/cost)/t
t→0
=lim 4(sint/t)/cost
t→0
=4·1/cos0
=4/1
=4
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