Introduction to Limits
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Transcript of Introduction to Limits
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Introduction to LimitsDoes limits of function exist?
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Description of limits
Limits come in all different shapes and sizes
Some functions have limits at all points, while others contain holes
Some functions may not have a limit at all
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Basic Limit Structure
x ⟶ c
The above limit is read as, “The limit of the function f (x) as x approaches c.”
Basically, this means that as x approaches some constant, f (x) will eventually become something;
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ExamplesEvaluate the following limits and tell whether
the limit exist.
lim 2x+3x ⟶ 1
lim 2x+3x ⟶ 0
lim 2x+3x ⟶ -3/2
= 2(1)+3=5, ∴ limit exists
= 2(0)+3=3, ∴ limit exists
= 2(-3/2)+3=0, ∴ limit exists
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When does the limit of a function not exist?
lim 2x+3x ⟶ -3 x+3
= -30
∴ limit does not exist
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Properties of limitsConstant
Scalar Multiple
Sum or difference
Product
Quotient
Power
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Techniques for Evaluating LIMITS
FISH
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Dividing Out Technique
lim x-6x ⟶ 6x2-36
(6)-6
(36)-36
0
0undefined
Factor
lim x-6x ⟶ 6
(X-6)(x+6)
1
(x+6)
1
(6+6)
1
12∴ limit exists
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Practice:
lim 5-xx ⟶ 515-3x
lim x2-81x ⟶ 9 9-x
lim x2-12x+36x ⟶ 1x2-7x+6
=⅓ , ∴ limit exists
=-18 , ∴ limit exists
= -5/0 , ∴ limit DOES NOT exist