Darryl Egley

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Section 1.5
Infinite Limits I 9/2
Infinite Limits II 9/2
Infinite Limits III 9/4
Infinite Limits IIII 9/4
Infinite Limits V 9/4
Infinite Limits VI 9/4
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Video lessons are here:

BELOW ARE ALL THE VIDEO LESSONS AND ASSIGNMENTS FOR EXAM IIII.

BELOW ARE ALL THE VIDEO LESSONS AND ASSIGNMENTS FOR EXAM III.

Calc I Chapter 3 Video Links
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Section 3.1
Extrema Intro I Intervals
Extrema Intro II Terminology
Extrema I
Extrema II
Extrema III Critical Values
Extrema Example I Polynomial
IMPORTANT NOTE: THERE IS AN ERROR IN THIS VIDEO. The solution to x-1=0 is not x = -1 (as I wrote). It is x = 1. this changes
the final result as well, since f(1) works out to be -1. Hence the Absolute minimum is at (1,-1)
Homework: Pg 171 #23 – 39 odd (omit #35) Note: For #33, the derivative does not exist at the cusp of the graph.
Review Topics to Help with Chapter 3 Homework Problems
Absolute Value and Derivatives
Section 3.1 #27, 33, 39
Section 3.1 #25, 31

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Section 3.2
Rolle’s Theorem
Mean Value Theorem
NOTE: There are no problems assigned from this section.

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Section 3.3
Increasing Decreasing Functions I
Increasing Decreasing Functions II
Increasing Decreasing Functions III
First Derivative Analysis Example I: Polynomial
First Derivative Analysis Example II: Rational
First Derivative Analysis Example III: Trigonometric
First Derivative Analysis Recap
Homework: Pg 187 #11, 15, 17, #19 – 31 odd, parts (a) & (b), #37 parts (a) & (b)
Selected Solutions:
Section 3.3 Page 187
Number 23
Number 27
Numbers 29 and 31
Numbers 41, 43, and 47

Graph Analysis Using f and f prime

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Section 3.4
Second Derivative Analysis I: Intro
Concavity
Inflection Points
Second Derivative Analysis Example I: Trigonometric
Homework: Pg 196 #5 – 13 odd, #17, 19, 21, 27, on these four items, find the inflection points, and the open intervals of concavity.
NOTE: Solutions to this Homework are Here
Second Derivative Test I: Intro Part A
Second Derivative Test II: Intro Part B
Second Derivative Test Example I: Polynomial
Second Derivative Test Example II: Polynomial
Second Derivative Test Example III: Polynomial

Second Derivative Test Example III: Polynomial – What If Scenario
Homework: Pg 196 #33, 35, 37
NOTE: Solutions to this Homework are Here

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Section 3.5
Limits at Infinity I
Limits at Infinity II
Limits at Infinity III
Limits at Infinity IIII
Homework: Pg 206 #13 – 23
NOTE: Solutions to this Homework are Here

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Section 3.7
Optimization I: Fences Down by the River
Optimization II: Fences Down by the River
Optimization III: Cut Corner Squares to Make a Box A
Optimization IIII: Cut Corner Squares to Make a Box B
SEE THE HOMEWORK BELOW. SOLUTIONS ARE COMING SOON
Here are some problems similar to the exam problems.
NOTE: Solutions to this Homework are Here

ABOVE ARE ALL THE VIDEO LESSONS AND ASSIGNMENTS FOR EXAM III.

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The lessons with content to be covered on Exam II are all BELOW this statement.
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Chapter 2:

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Section 2.1
Definition of the Derivative I
Definition of the Derivative II
Derivative Using the Definition – Example I
Derivative Using the Definition – Example II
Alternative Derivative Form I
Definition vs Alternate Form I
Derivative of Absolute Value
Pg 107
#9, 11, 13 (use the “Alternate Derivative Form” for these)
#17, 19, 21, 25, 27 (use the “Definition of the Derivative” for these)
#29, 31, 33 (do part a only on these)

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Section 2.2
Basic Derivative Rules I
Proof of Power Rule
Basic Derivative Rules II
Derivative of sin(x) and cos(x)
Homework: Pg 118 #7-26, #31-38, 39-54

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Section 2.3
Product Rule
Proof of Product Rule
Quotient Rule
Derivatives of the Trig Functions
Homework: Pg 129 #29 – 55 odd, 63(a), 65(a), 69, 71
Higher Order Derivatives
Homework: Pg 131 #91-100

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Section 2.4
Chain Rule I
Chain Rule II – Examples
Chain Rule III – More Examples
Homework: Pg 140 #9-53 odd, #71,73,75

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Section 2.5
Implicit Differentiation Intro
Implicit Differentiation I
Implicit Differentiation II
Implicit Differentiation Examples I
Note: The above video got cut off short for some reason.
Here is the second example from it worked out completely 10/7.
There also are some straggler scores from Exam I which will get posted Wednesday, too.
Implicit Differentiation Examples II
Implicit Differentiation Multiple Variables
Homework: Pg 149 #5-19 odd, #25-39 odd #45

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Section 2.6
Related Rates Intro
Related Rates Example I Sphere
Related Rates Example II Conical Pile of Sand I 10/4
Related Rates Example III Conical Pile of Sand II 10/4
Related Rates Example IIII Sliding Ladder I 10/4
Related Rates Example IIII Sliding Ladder II 10/4
Related Rates Example V Angle of Elevation 10/4
Homework: Pg 157 #11, 13a, 15, 17, 21a b & c, 25a,

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The lessons with content to be covered on Exam II are all ABOVE this statement.

The lessons with content to be covered on Exam I are all BELOW this statement.

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Chapter 1
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Section 1.2
Introduction to Calculus Part I
Introduction to Calculus Part II
Limits I
Limits II
Limits III
Limits IIII
Limits V
Limit Example I
Limit Example II
Limit Example III
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Section 1.3
Evaluating Limits – Theorems
Evaluating Limits – Trigonometry
Evaluating Limits – Indeterminate Forms I
Evaluating Limits – Indeterminate Forms II Conjugates
Evaluating Limits – Indeterminate Forms III Fractions
Squeezing Theorem I
Squeezing Theorem II
Special Limit Property I
Special Limits – Difference Quotient Example I
Special Limits – Difference Quotient Example II
Special Limits – Difference Quotient Example III

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Section 1.4
Continuity I
NOTE: There is an error in the “Continuity I” video at the 12:55 time mark.
The function I use is x squared minus 4 rather than x squared minus x.
The final result is 12 either way, and the function is continuous either way, but it’s still an error.
Continuity II
One-Sided Limits I
Properties of Continuity
Find the Discontinuity I
Find the Discontinuity II
Find the Discontinuity III
Homework: Pg 84, #39-52, #59-61
Solutions to this homework are Here.
I copied problem #51 wrong. Please ignore my solution.

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Section 1.5
Infinite Limits I 9/2
Infinite Limits II 9/2
Infinite Limits III 9/4
Infinite Limits IIII 9/4
Infinite Limits V 9/4
Infinite Limits VI 9/4
Homework: 92 #37 – 45

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