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Finding limits from graphs
- Lesson: 1a12:00
- Lesson: 1b3:01
- Lesson: 1c2:41
- Lesson: 1d2:17
- Lesson: 1e2:30
Finding limits from graphs
Limit is an important instrument that helps us understand ideas in the realm of Calculus. In this section, we will learn how to find the limit of a function graphically using one-sided limits and two-sided limits.
Lessons
DEFINITION:
left-hand limit: limx→a−f(x)=L
We say "the limit of f(x), as x approaches a from the negative direction, equals L".
It means that the value of f(x) becomes closer and closer to L as x approaches a from the left, but x is not equal to a.
DEFINITION:
right-hand limit: limx→a+f(x)=L
We say "the limit of f(x), as x approaches a from the positive direction, equals L".
It means that the value of f(x) becomes closer and closer to L as x approaches a from the right, but x is not equal to a.
DEFINITION:
limx→af(x)=L if and only if limx→a+f(x)=L and limx→a−f(x)=L
left-hand limit: limx→a−f(x)=L
We say "the limit of f(x), as x approaches a from the negative direction, equals L".
It means that the value of f(x) becomes closer and closer to L as x approaches a from the left, but x is not equal to a.
DEFINITION:
right-hand limit: limx→a+f(x)=L
We say "the limit of f(x), as x approaches a from the positive direction, equals L".
It means that the value of f(x) becomes closer and closer to L as x approaches a from the right, but x is not equal to a.
DEFINITION:
limx→af(x)=L if and only if limx→a+f(x)=L and limx→a−f(x)=L
- 1.For the function f whose graph is shown, state the following:
a)limx→−5−f(x)
limx→−5+f(x)
limx→−5f(x)
f(−5)b)limx→−2−f(x)
limx→−2+f(x)
limx→−2f(x)
f(−2)c)limx→1−f(x)
limx→1+f(x)
limx→1f(x)
f(1)d)limx→4−f(x)
limx→4+f(x)
limx→4f(x)
f(4)e)limx→5−f(x)
limx→5+f(x)
limx→5f(x)
f(5)
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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