Math 131		Final Review Sheet		2 May

I will hold an optional review session Tu. at 9 AM in Science 112.

The comprehensive departmental final is Wed. from 330 PM to 530 PM in 
Science 214.  The final has 2 parts.  The first part is completely calculator 
free and constitutes more than half the final.  The second part requires the 
use of your graphing calculator.  You should bring paper, graph paper and 
a graphing calculator to the final.

Calculus is the study of two operations of functions called 
differentiation and integration.  These are inverse operations by
the FUNdamental Theorem of Calculus.

Use the rule of four to describe each key concept of the course.

FUNctions (Chapter 1)
For each named function below identify its domain, range, graph and other 
    key properties.
	linear	
	exponential	logarithmic
	trigonometric (sine, cosine and tangent) inverse trigonometric
	power	polynomial	rational

Determine whether a set of points can fit a particular model.
Determine half life or doubling time for an exponential model.
Determine an exponential model given two points.
Solve equations exactly using logarithms.

Derivative (Chapter 2)
Explain an average rate of change.
Explain an instantaneous rate of change.
Distinguish between the above two rates.
Define the derivative of a function.
Define the difference quotient.
Evaluate a particular difference quotient.
Explain the secant line for a function.
Explain the tangent line for a function.
Describe the connection between secant line and tangent line for a function.
Explain the second derivative.

Rules for derivatives (Chapter 3)
Know the following rules for derivatives:
	sum	difference	product		quotient
	chain
	power
	sine	cosine	tangent	arcsin	arctan
	e^x	a^x	ln	log
Explain the tangent line approximation to a function at a point.
Compute a tangent line approximation to a function at a point.
Explain L'Hopital's rule.
	 
Applications of the derivative (Chapter 4)
Describe local and global maxima and minima.
Describe first derivative test for local maxima and minima.
Describe second derivative test for local maxima and minima.
Explain a critical point of a function.
Explain an inflection point of a function.
Graph a function accurately with calculus (and without a calculator).
Solve a applied optimization problem with calculus.
Use calculus to analyze a family of curves.

Definite integral (Chapter 5)
Define the definite integral.
Explain the connection between the definite integral and area.
Define left and right hand sums.
Evaluate a particular left and right hand sum with a calculator.
Explain average value of a function on an interval.
Identify key properties of the definite integral.
State precisely the FUNdamental Theorem of Calculus 
Compute a definite integral with the fundamental theorem.

Constructing antiderivatives (Chapter 6)
Define an antiderivative.
Find an antiderivative for a particular function.
Know antiderivative rules.
	power    ln
	exponential
	sine	cosine	tangent	arcsin	arctan


Review problems
Ch. 1 p.  58 # 1 3 4 5 7 9 11 13 16 17 19 21 25 27 29 31 35 37 39 41 47 49 53
Ch. 2 p. 103 # 3 5 7 11 13 15 17 21 25 29 
Ch. 3 p. 159 # 3 7 11 15 19 23 27 33 45 51 61 67 69 83 95 101
Ch. 4 p. 230 # 3 5 9 11 13 15 19 25 31 35 37 39
Ch. 5 p. 272 # 1 3 7 9 11 15 21 25 29 
Ch. 6 p. 306 # 3 7 11 13 15 19 23 33 41 47