- (2.6)James Stewart Calculus 5th
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- (11.1)James Stewart Calculus 5th
- (10.5)James Stewart Calculus 5th
- (10.6)James Stewart Calculus 5th
- (10.2)James Stewart Calculus 5th
- (10.4)James Stewart Calculus 5th
- (11.2)James Stewart Calculus 5th
- (10.1)James Stewart Calculus 5th
- (8.4)James Stewart Calculus 5th
Limits at Infinity:Horizontal Asymptotes水平渐近线
通过下面的例子,来探究
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有对应的表格:
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- 对应的图像
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- 得出结论:
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- 定理:
当x越来越大的时候, 对应的 f(x) 越接近 L
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- 读法:
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- 对应的例子:
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定理2
也就是到 负无穷大
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定理3 (horizontal asymptote 水平渐近线)
只要满足一个, 就可以 y = L, 就是 水平渐近线
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定理4 tan的水平渐近线
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定理5
这个定理,很容易推理,有理数r>0的时候,很容易证明,略
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定理6
其实,这里不一定是e, 只要 大于1的数就行
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Infinite Limits at Infinity 极限处为无穷大
大体,只要满足下面一个即可
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Precise Definitions 精确的定义
具体的精确定义,其实也就是 ε,L,无穷大等的定义
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对应的图像:
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也就是, 取 x > N, 都有 对应的 |f(x) - L| < ε
定理8
当然,也会有对应的
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对应的图像:
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定理9
其实,和 定理7 差不多, 只是一个是 无穷大, 一个是 L
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同理类似定理8, 可以得到 负无穷大
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