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- Limits
Finding limits algebraically - direct substitution
- Intro Lesson: a13:20
- Lesson: 1a2:03
- Lesson: 1b3:00
- Lesson: 1c3:31
- Lesson: 1d6:07
- Lesson: 2a2:41
- Lesson: 2b6:03
- Lesson: 35:51
- Lesson: 48:33
Finding limits algebraically - direct substitution
Graphically finding the limit of a function is not always easy, as an alternative, we now shift our focus to finding the limit of a function algebraically. In this section, we will learn how to apply direct substitution to evaluate the limit of a function.
Lessons
• if: a function f is continuous at a number a
then: direct substitution can be applied: limx→a−f(x)=limx→a+f(x)=limx→af(x)=f(a)
• Polynomial functions are continuous everywhere, therefore "direct substitution" can ALWAYS be applied to evaluate limits at any number.
then: direct substitution can be applied: limx→a−f(x)=limx→a+f(x)=limx→af(x)=f(a)
• Polynomial functions are continuous everywhere, therefore "direct substitution" can ALWAYS be applied to evaluate limits at any number.
- IntroductionNo more finding limits "graphically"; Now, finding limits "algebraically"!a)What is Direct Substitution?
- 1.Evaluate the limit:a)limx→3(5x2−20x+17)b)limx→−25−4xx3+3x2−1c)limx→0∣x∣d)limx→2π2−cosxsinx
- 2.Evaluate the one-sided limit:a)limx→3−(5x2−20x+17)
limx→3+(5x2−20x+17)b)limx→4−x−4
limx→4+x−4 - 3.
- 4.
a)limx→−1−g(x)
limx→−1+g(x)
limx→−1g(x)b)limx→4−g(x)
limx→4+g(x)
limx→4g(x)
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1.
Limits
1.1
Introduction to Calculus - Limits
1.2
Finding limits from graphs
1.3
Limit laws
1.4
Continuity
1.5
Finding limits algebraically - direct substitution
1.6
Finding limits algebraically - when direct substitution is not possible
1.7
Infinite limits - vertical asymptotes
1.8
Limits at infinity - horizontal asymptotes
1.9
Intermediate value theorem
1.10
Squeeze theorem
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Practice topics for Limits
1.2
Finding limits from graphs
1.4
Continuity
1.5
Finding limits algebraically - direct substitution
1.6
Finding limits algebraically - when direct substitution is not possible
1.7
Infinite limits - vertical asymptotes
1.8
Limits at infinity - horizontal asymptotes
1.9
Intermediate value theorem
1.10
Squeeze theorem