Intro to Limits.pdf
January 28, 2013
EQ: How do we find one and two sided limits using a graph?
Warm Up: What can you infer about these limits using the tables you filled in?
x
1.9
1.99
1.999
2.001
2.01
2.1
­0.1
­0.01
­0.001
0.001
0.01
0.1
f(x)
x
f(x)
1
Intro to Limits.pdf
January 28, 2013
EQ: How do we find one and two sided limits using a graph?
Make a table or use a graphing calculator to find the limit.
x
f(x)
2
Intro to Limits.pdf
January 28, 2013
EQ: How do we find one and two sided limits using a graph?
• The process of approximang the value of f(x) by using the surrounding values is called find finding the limit .
• In order to find the limit of a funcon when x = a, the values that we use to approximate f(a) must be sufficiently close to f(a) .
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Intro to Limits.pdf
January 28, 2013
EQ: How do we find one and two sided limits using a graph?
Limit Notaon
limx→a f(x) = L
• When we solve for limits, we know values of x, and we're solving for values of y!
• There are two types of limits
• one‐sided limits
• two‐sided limits.
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Intro to Limits.pdf
January 28, 2013
One‐Sided Limits
Le‐hand Limits
The limit of f(x) as x
approaches a from the le is
equal to some number L. Right‐hand Limits
The limit of f(x) as x
approaches a from the right is
equal to some number L. EQ: How do we find one and two sided limits using a graph?
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Intro to Limits.pdf
January 28, 2013
Two‐Sided Limits The limit of f(x) as x approaches a [from the le and the right] equals some number L.
EQ: How do we find one and two sided limits using a graph?
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Intro to Limits.pdf
January 28, 2013
Decoding Limit Notaon
1. lim x→5 x + 6 = 11
2. lim x→2 2x ‐ 4 = 0
3.
4.
EQ: How do we find one and two sided limits using a graph?
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Intro to Limits.pdf
January 28, 2013
Your Turn:
Explain what each equaon means:
5. 6. 7. limx→6 x2 = 36
EQ: How do we find one and two sided limits using a graph?
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Intro to Limits.pdf
January 28, 2013
• f(0) = • What is the value of f(x) as x approaches 0 from the le?
• What is the value of f(x) as x approaches 0 from the right?
• What is the value of f(x) as x approaches 0 [from both direcons]?
EQ: How do we find one and two sided limits using a graph?
9
Intro to Limits.pdf
January 28, 2013
• f(0) = • What is the value of f(x) as x approaches 0 from the right?
• What is the value of f(x) as x approaches 0 from the le?
• What is the value of f(x) as x approaches 0 [from both direcons]?
EQ: How do we find one and two sided limits using a graph?
10
Intro to Limits.pdf
January 28, 2013
• f(0) = • • • EQ: How do we find one and two sided limits using a graph?
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Intro to Limits.pdf
January 28, 2013
• f(0) = • • • EQ: How do we find one and two sided limits using a graph?
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Intro to Limits.pdf
January 28, 2013
EQ: How do we find one and two sided limits using a graph?
13
Intro to Limits.pdf
January 28, 2013
Your Turn:
Complete parts A ‐ D for problems 1 ‐ 3,
1.
A.
B.
C.
D.
EQ: How do we find one and two sided limits using a graph?
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Intro to Limits.pdf
January 28, 2013
2.
A.
B.
C.
D.
EQ: How do we find one and two sided limits using a graph?
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Intro to Limits.pdf
January 28, 2013
EQ: How do we find one and two sided limits using a graph?
3.
A. B.
C.
D.
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Intro to Limits.pdf
January 28, 2013
EQ: How do we find one and two sided limits using a graph?
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Intro to Limits.pdf
January 28, 2013
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