Feg 1034 Calculus & Analysis 1
Essay by Sanjeetha • December 6, 2017 • Research Paper • 1,195 Words (5 Pages) • 973 Views
FEG 1034 Calculus 1 Chapter 02[pic 1]
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Chapter 2
Function and limit
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FEG 1034 Calculus & Analysis 1
FEG 1034 Calculus 1 Chapter 05[pic 4]
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What thing will come out in Final
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2.1 Limit
- Vertical Asymptotes
- Horizontal Asymptotes
2.2 Inverse Function
- Characteristic of inverse function
- Horizontal test
- Second derivative test
2.3 Derivative of inverse function
FEG 1034 Calculus & Analysis 1 2
FEG 1034 Calculus 1 Chapter 02[pic 7]
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2.1 Limit
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= 3−1 and = 2 + + 1
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−1
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Both graph are the same, but just that can’t include = 1, which is not continuous when = 1.
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FEG 1034 Calculus & Analysis 1 3
FEG 1034 Calculus 1 Chapter 02[pic 15]
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2.1.1 Vertical Asymptotes
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How to determine the vertical asymptotes?
- Check the existence of denominator (must be simplify)
- Check the value to make denominator become zero, hence make the function become undefined.
For this example, the vertical asymptotes is in = 2.
FEG 1034 Calculus & Analysis 1 4
FEG 1034 Calculus 1 Chapter 02[pic 18]
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Example 1 – find vertical asymptotes
Find the vertical asymptotes for the functions.
a). = 1
b). = 1
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FEG 1034 Calculus & Analysis 1 5
FEG 1034 Calculus 1 Chapter 02[pic 21]
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2.1.2 Horizontal Asymptotes
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How to determine the horizontal asymptotes?
- If the limit at infinite is defined, then there is the horizontal asymptotes.
=
For this example,
3 | |||||||
lim | = −0 | 3 | = 0 | ||||
→−∞ −2 | −∞ |
lim 3 = 0
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→+∞ −2
3
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+∞ = 0
horizontal asymptotes
at = .
FEG 1034 Calculus & Analysis 1 6
FEG 1034 Calculus 1 Chapter 02[pic 30]
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Example 2 – find horizontal asymptotes
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Find the horizontal asymptotes for the functions.
2 + 1 | 2 | 1 | 1 | |||||||||||||||
= | = 1 + | = 1 − | + | |||||||||||||||
2 − 1 | 2 − 1 | + 1 | − 1 | = | ||||||||||||||
lim | 2 | + 1 | = 1 + | lim | − | 1 | + | 1 | = 1 | |||||||||
− 1 | + 1 | − 1 | ||||||||||||||||
→−∞ 2 | →−∞ | |||||||||||||||||
lim | 2 | + 1 | = 1 + | lim | − | 1 | + | 1 | = 1 | |||||||||
− 1 | + 1 | − 1 | ||||||||||||||||
→+∞ 2 | →+∞ |
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