Limit laws
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- Lesson: 1a6:40
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- Lesson: 2a4:55
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Limit laws
Basic Concepts: Function notation
Lessons
Here are some properties of limits:
1) limx→ax=a
2) limx→ac=c
3) limx→a[cf(x)]=climx→af(x)
4) limx→a[f(x)±g(x)]=limx→af(x)±limx→ag(x)
5) limx→a[f(x)g(x)]=limx→af(x)limx→ag(x)
6) limx→ag(x)f(x)=limx→ag(x)limx→af(x), only if limx→ag(x)≠0
7) limx→a[f(x)]n=[limx→af(x)]n
Where c is a constant, limx→af(x) and limx→ag(x) exist.
Here is a fact that may be useful to you.
If P(x) is a polynomial, then
limx→aP(x)=P(a)
1) limx→ax=a
2) limx→ac=c
3) limx→a[cf(x)]=climx→af(x)
4) limx→a[f(x)±g(x)]=limx→af(x)±limx→ag(x)
5) limx→a[f(x)g(x)]=limx→af(x)limx→ag(x)
6) limx→ag(x)f(x)=limx→ag(x)limx→af(x), only if limx→ag(x)≠0
7) limx→a[f(x)]n=[limx→af(x)]n
Where c is a constant, limx→af(x) and limx→ag(x) exist.
Here is a fact that may be useful to you.
If P(x) is a polynomial, then
limx→aP(x)=P(a)
- IntroductionLimit Laws Overview:
7 Properties of Limit Laws - 1.Evaluating Limits of Functions
Evaluate the following limits using the property of limits:a)limx→2x2+4x+3b)limx→23(x2+4x+3)2c)limx→12+x42−3x+4x2d)limx→04(3)xe)limx→2π3(sinx)4 - 2.Evaluating Limits with specific limits given
Given that limx→5f(x)=−3, limx→5g(x)=5, limx→5h(x)=2, use the limit properties to compute the following limits:a)limx→5[5f(x)−2g(x)]b)limx→5[g(x)f(x)+3h(x)]c)limx→5h(x)2g(x)d)limx→5g(x)5[f(x)]3
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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