Math 120

Winter 2009

Handouts from Recitation

Instructor: 
Dale Winter
6124 Wean Hall
(412) 268-8419
amanita@andrew.cmu.edu

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The handouts distributed and used in Tuesday recitation sections are listed in the table below.

Click on the title of the handout to download a copy in PDF format.

Date Title Summary Solutions
January 20 Finding formulas for functions
  • Finding formulas for linear functions
  • Solving linear equations
  • Calculating the intersection point of two linear functions
  • Using the concept of domain and common sense to determine the domains of the pieces of a function defined in pieces
  • Writing an equation for a horizontal line
Answers for recitation activity
January 27 Finding limits involving infinity
  • Graphing functions that involve exponentials
  • Finding evidence for limits from graphs and tables
  • Using the algebraic structure of a function to determine the limit as x becomes infinite
Answers for recitation activity
February 3 Interpreting rates of change
  • Understanding economic measures of income distribution
  • Interpreting a graph showing the rate of change
  • Examining the validity of political claims about America's economic crises
Answers for recitation activity
February 10 Practice at setting up problems and applications of the Chain Rule
  • Using trigonometric functions (sin, cos, tan) and Pythagoras to set up formulas
  • Comprhending how physical measurements (distance, speed) can be represented using functions and derivatives
  • Using the Chain Rule to relate an unknown derivative to a known derivative
Answers for recitation activity
February 24 Setting up and using Exponential Functions
  • Setting up a formula for an exponential function based on a word problem
  • Alternative formulas for the growth factor in an exponential function
  • Making predictions using exponential functions
Answers for recitation activity
March 3 The Law of Forgetting
  • Collating and analyzing data from a psychology experiment
  • Calculating rates of change
  • Creating a differential equation from data
There are no solutions for this recitation activity - the numbers you come up with will depend on your pariticipation in the psychological experiment conducted in class from February 25 to March 2.
March 17 L'Hopital's Boot Camp
  • Learning to use L'Hopital's rule to calculate limits
  • Learning to recognize when (and when not) to apply L'Hopital's rule
  • Manipulating limits so that L'Hopital's rule can be applied to evaluate them
Answers for recitation activity
March 24 Introduction to Constrained Optimization
  • Finding formulas using areas and volumes
  • Identifying constraints and writing them as mathematical equations
  • Using derivatives to find the turning points of a function
  • Using the first derivative to classify the turning points as local maximums or local minimums
Answers for recitation activity
March 31 More Problems on Constrained Optimization
  • Finding formulas using areas and volumes
  • Identifying constraints and writing them as mathematical equations
  • Using derivatives to find the turning points of a function
  • Using the first derivative to classify the turning points as local maximums or local minimums
  • Using the second derivative to classify the turning points as local maximums or local minimums
Answers for recitation activity
April 7 Curve Sketching and Interpretive Dance
  • Sketching the graph of a derivative from the graph of a function
  • Reconstructing the graph of a function from the graph of a derivative
  • Reconstructing the graph of a function from the signs of the first and second derivatives
  • Understanding the relationship between distance, velocity and acceleration
  • Inventing interpretive dances to represent distance-time graphs
Answers for recitation activity
April 14 Integrating functions from the numerical, algebraic and symbolic points of view
  • Calculating approximate function values using Euler's method
  • Sketching the graph of a function from the graph of a derivative
  • Finding a formula for an antiderivative
Answers for recitation activity
April 21 Additional practice setting up and solving word problems
  • Setting up related rates problems
  • Solving related rates problems
  • Setting up optimization problems
  • Solving optimization problems
You really need to attend this recitation to receive the benefit