Calculus with Polynomials

  Math 170, 12:00 AM - 12:50 PM, Monday, Wednesday, Friday in Higgins Hall 107

 

    9 AM: The course syllabus     (a pdf version syllabus.pdf )
    10 AM: The course syllabus     (a pdf version syllabus.pdf )

   A free online College Algebra Book by Stitz and Zeager.  There is an online version with

links and a dpf that you can down load. 
Here is a link to a copy of the online version stored on my webpage in case theirs is slow.

For the next quiz you want to identify where quadratics and cubics are increasing, just as we have
been doing in class and just as you did in your homework.
Here are some examples.  Quadratic examples and Cubic examples.  (I will update these.)

Old Exams

Exam 1a,    Key 1a
Exam 1b,    Key 1b
Exam 1c,    Key 1c

Old Quizzes

Quiz 1a, Quiz 1b                Key 1a,  Key 1b
Quiz 2a, Quiz 2b, Quiz2c   Key 2a,  Key 2b, Key 2c
Quiz 3a, Quiz 3b, Quiz 3c  Key 3a,  Key 3b, Key 3c
Quiz 4a, Quiz 4b, Quiz 4c  Key 4a,  Key 4b
Quiz 5a, Quiz 5b, Quiz 5c  Key 5a,  Key 5b, Key 5c
Quiz 6a, Quiz 6b                Key 6a,  Key 6b

Quiz 7a, Quiz 7b                      Key 7a,  Key 7b
Quiz 8a, Quiz 8b, Quiz8c         Key 8a,  Key 8b, Key 8c
Quiz 9a, Quiz 9b,                     Key 9a,  Key 9b
Quiz 10a, Quiz 10b                  Key 10a,  Key 10b
Quiz 11a, Quiz 11b, Quiz 11c  Key 11a,  Key 11b, Key 11c


Assignments

 

Topics

Problems

Summary

Quiz Topics

 

Lines (Review)

(JIT) § 4.2:  problems 1-19 odd
(SZ) § 2.1 (p101): problems 1 and 2

Be able to find the equations of lines using point slope form, to be able to go from point-slope to slope-intercept to general forms of the lines. Be able to graph lines.

Q1

Quadratics (Review)
 (SZ) § 2.3 (p129): problems 1 and 9 Be able to graph quadratic functions and solve quadratic equations.
 Q1

Relations
(SZ) § 1.1: # 2a,2c,2f (Symmetry)
§ 1.2: 1a,1c,2a,2d

Know what a Relation is,
know how to identify symmetry propoerties in Relations.
 Q2

Graphs of Equations
(SZ) § 1.3 : 1a, 1b, 1e
Know what the graph of an Equations is and how to identify the symmetry
 Q2

Graphs of Functions
(SZ) § 1.4: 1a, 1b, 1c, 1e, 2c, 2d, 2g, 2h, 3.
What is a function and How can you identify function from it's graph
 Q2

Functions Domains
and Arithmetic
 (SZ) § 1.5: 5,7,8 and § 1.6: 1,2
(TC) p8: 1,3,5,7
 Be able to evaluate functions and to identify the implied domain of functions and their arithmetic combinations.
 Q3

Piecewise defined functions (TC) page 6:  problems 23,25,27,29
worksheet

Be able to go from Graphs to Rules and from Rules to Graphs
  Slope Functions for Quadratics and Where are quadratics increasing? Quadratic Material Also, Slope functions for quadratics  
  Slope Functions for Cubics and Where are cubics increasing Cubic Material    

Slope Function Power Rule
(TC)  p160-1: Problems 1-37 (except 23,27,35)
 Power Materials
 TC Reading, Section 3.2

 

Product Rule

see above

 Product Materials
  Quotient Rule see above Quotient Materials Answers
  Test I Materials Monday, October 19th, 2009    
         
    Generalized Power Rule
 (TC § 3.5) p199: problems 9,11,13,23,31,33,61  Materials
  

Implicit Differentiation
 (TC § 3.6) p209: problems 3,5,7,19,21,23


Related Rates: Right Triangles/Cars
 (TC § 3.9) p236: problems 7,13a,13b,14,15,23,34,36

  RR: Tanks (TC § 3.9) p236: 17,18,19,24,21    
  RR: Shadows (TC § 3.9) p236: 30,31    
  Tangents and Derivatives (TC § 2.7) p137: problems 11-21,23,26  quadratics,  fractions,and radicals tangent line material (easier)
  
       quadratics,  fractions, and radicals tangent line material
  

 

 Tangent Lines   Tangent Lines S&P



Extrema
 (TC § 4.1): problems 15, 17, 19, 21, 23, 35, 55, 57



(TC § 4.3): problems 1-27 odd, Parts a and c
The first derivative test
         
         
         
  EXAM II,  MONDAY, November 23rd, 2009 That is before Tday    
         

 

Properties of Functions

(TC) p17: probs 11,13,15,17 two more problems

Make a list of function properties.  Be able to identify these properties on the graph of a function.

 

 

Shifting and Scaling Functions (TC) p23-25

(TC) p28: probs 15,16,17,18 and 17-27 odd and 51-54 odd  new page

Be able to make new functions from old functions by shifting horizontally and vertically and by rescaling horizontally and vertically.  This can be done both algebraically and graphically.

 

 

Limits

(TC) p76: probs 1,2,3,4,11,13

 

 

 

Finding Limits Algebraically

(TC) p83: problems 1,5,9,...,33 (every 4th)

Be able to use algebraic techniques to find limits.  Key is the division of polynomials and the use of conjugates to simplify fractions.


 

One sided limits

(TC) p106  problems:1,3

 

 

 

Limit Rule Game

(TC) p108: problems 11,13,14,17

 

 

 

Limits as x goes to infinity

(TC) p108: problems 37,39,41,51, 53,55,57,61

 

 

 

Infinite Limits and Vertical Asymptotes

(TC) p117: 1-11 odd, 17,19,21,39,41

 

 

 

Continuity

(TC) p129: 2,4,35,39

 

 

 

 

 

 

 

Drawing Derivatives
Practice






Derivatives
 (TC) p167: 1-11 odd, 17,19,21,29,31,33,35,37


Increasing,Decreasing
 (TC) p289: 1-27 odd, Part b An increasing, decreasing Poem.

Extrema  



(TC) p273: 39-47 odd, 55, 57
 The second derivative test

Optimization
 (TC) p309: 1-5,1,8,11,14