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Infinite limits - vertical asymptotes
- Intro Lesson: a14:00
- Intro Lesson: b5:49
- Intro Lesson: c29:05
- Lesson: 1a1:49
- Lesson: 1b1:34
- Lesson: 1c1:08
- Lesson: 1d1:31
- Lesson: 2a6:23
- Lesson: 2b6:06
- Lesson: 36:49
- Lesson: 40:55
Infinite limits - vertical asymptotes
Limits don't always necessarily give numerical solutions. What happens if we take the limit of a function near its vertical asymptotes? We will answer this question in this section, as well as exploring the idea of infinite limits using one-sided limits and two-sided limits.
Lessons
i) limx→a−f(x)=∞ |
ii) limx→a+f(x)=∞ |
iii) limx→a−f(x)=,−∞ |
iv) limx→a+f(x)=,−∞ |
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- IntroductionIntroduction to Vertical Asymptotesa)finite limits VS. infinite limitsb)infinite limits translate to vertical asymptotes on the graph of a functionc)vertical asymptotes and curve sketching
- 1.Determine Infinite Limits Graphically
For the function f whose graph is shown, state the following:a)limx→−4−f(x)
limx→−4+f(x)
limx→−4f(x)b)limx→1−f(x)
limx→1+f(x)
limx→1f(x)c)limx→3−f(x)
limx→3+f(x)
limx→3f(x)d)limx→5−f(x)
limx→5+f(x)
limx→5f(x) - 2.Evaluate Infinite Limits Algebraically
Find:a)limx→0−x1
limx→0+x1
limx→0x1b)limx→0−x21
limx→0+x21
limx→0x21 - 3.Evaluate Limits Algebraically
Find:
limx→2−x−25x
limx→2+x−25x
limx→2x−25x - 4.Determine Infinite Limits of Log Functions
Determine:
limx→0+lnx
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16.
Limits
16.1
Finding limits from graphs
16.2
Continuity
16.3
Finding limits algebraically - direct substitution
16.4
Finding limits algebraically - when direct substitution is not possible
16.5
Infinite limits - vertical asymptotes
16.6
Limits at infinity - horizontal asymptotes
16.7
Intermediate value theorem
16.8
Squeeze theorem
Don't just watch, practice makes perfect
Practice topics for Limits
16.1
Finding limits from graphs
16.2
Continuity
16.3
Finding limits algebraically - direct substitution
16.4
Finding limits algebraically - when direct substitution is not possible
16.5
Infinite limits - vertical asymptotes
16.6
Limits at infinity - horizontal asymptotes
16.7
Intermediate value theorem
16.8
Squeeze theorem