3_Properties_Limits_v2.notebook 1 September 10, 2019 Properties of Limits Lesson objectives Teachers' notes Topic 1.5: Determining Limits Using Algebraic Properties of Limits LIM1: Reasoning with definitions, theorems, and properties can be used to justify claims about limits. LIM1.D: Determine the limits of functions using limit theorems. LIM1.D.1: Onesided limits can be determined analytically or graphically. LIM1.D.2: Limits of sums, differences, products, quotients, and composite functions can be found using limit theorems. Teachers' notes Lesson objectives Subject: Topic: Grade(s): Prior knowledge: Crosscurricular link(s): Type text here Type text here Type text here Type text here Type text here Lesson notes: Type text here
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3_Properties_Limits_v2.notebook
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Properties of Limits
Lesson objectives Teachers' notes
Topic 1.5: Determining Limits Using Algebraic Properties of Limits
LIM1: Reasoning with definitions, theorems, and properties can be used to justify claims about limits.
LIM1.D: Determine the limits of functions using limit theorems.
LIM1.D.1: Onesided limits can be determined analytically or graphically.
LIM1.D.2: Limits of sums, differences, products, quotients, and composite functions can be found using limit theorems.
Teachers' notesLesson objectives
Subject:
Topic:
Grade(s):
Prior knowledge:
Crosscurricular link(s):
Type text here
Type text here
Type text here
Type text here
Type text here
Lesson notes:
Type text here
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There will be times when you need to consider limits of functions symbolically, such as, f(x), g(x), and h(x) . When you are given combinations, compositions, and other modifications of these nonspecific functions, there are some important properties of limits that will prove essential to these general function types.
Lesson 3: Properties of Limits
Topic 1.5: Determining Limits Using Algebraic Properties of Limits
LIMIT PROPERTIES
Let b and c be real numbers, let n be a positive integer, and let f and g be functions.
1. Constant Rule: 2. Identity Rule:
3. Coefficient Rule: 4. Sum or Difference Rule:
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5. Product Rule:
6. Quotient Rule:
7. Power Rule: n is rational
8. Composite Function Rule:
9. Root Rule:
if the root on the right side exists.
Being skilled at reciting these rules in English will help you truly understand them. For example, The Sum or Difference Rule can be stated as “The limit of a sum (difference) is the sum (difference) of the limits. Can you give a description for each property in your own words?
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A. B.
C. D.
EX#1: Use the properties of limits to find each of the following limits. If a limit does not exist, state why.
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E. F.
G. H.
J. K.
EX #2: Find the limits if , ,
A.
C.
B.
and
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F.
E. D.
EX #3: Given and then find the following:
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A. Given and
find
EX #4: Find the limits of the following composition functions.
B. Given and
find
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EX #5: Use the graphs of and below to find the limits.
A. B.
C. D.
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