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AP Calculus
AB Correlations
BC Correlations
5th Six Weeks Assignment
Calculating limits using algebra
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Calculating Limits Using Algebra
Use of Direct Substitution
This idea states that this function is continuous at whatever value c may be
Some Basic Limits
 Let b and c be real numbers and let n be a positive integer.
Examples:
Properties of Limits
Let b and c be real numbers, let n be a positive integer. and let f and g be functions with the following limits
1.
Scalar multiple:
2.
Sum or difference:
3.
Product
4.
Quotient
K cannot equal 0
5.
Power
Example of a Limit of a Polynomial
The Limit of a Rational Function
Limits of Trigonometric Functions
1.
2.
3.
4.
5.
6.
Functions That Agree at All But One Point
Notice that if you apply the limit as is the denominator will equal 0 which is not allowed. You must factor out the numerator to solve this limit
Cancel out the (x1) from the top and bottom by division and all you are left with is
Source Calculus with Analytic Geometry Eighth Edition. Houghton Mifflin Company, Boston/New York
example calculating limits using algebra
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 Use of Direct Substitution
This idea states that this function is continuous at whatever value c may beSome Basic Limits
 Let b and c be real numbers and let n be a positive integer.
Examples:
Properties of Limits
Let b and c be real numbers, let n be a positive integer. and let f and g be functions with the following limits
1.Scalar multiple:
2. Sum or difference:
3. Product
4. Quotient
K cannot equal 0
5. Power
Example of a Limit of a Polynomial
The Limit of a Rational Function
Limits of Trigonometric Functions
1.
2.
3.
4.
5.
6.
Functions That Agree at All But One Point
Notice that if you apply the limit as is the denominator will equal 0 which is not allowed. You must factor out the numerator to solve this limit
Cancel out the (x1) from the top and bottom by division and all you are left with is
Source Calculus with Analytic Geometry Eighth Edition. Houghton Mifflin Company, Boston/New York
example calculating limits using algebra