Final Exam Topics

MATH 117 Section FG
Topics for Final Exam

Section	Topics	Suggested Problems
4.6	Graphing with technology Using calculus to be more accurate	3, 6, 7, 8, 17, 19, 21 9, 11, 23
4.7	Setting up optimization problems Finding critical values First Derivative Test	2, 5, 6, 9, 10, 13, 14, 30, 32, 55, 57 7, 11, 17, 21, 53
4.8	Geometric meaning of Newton’s method Approximating solutions with Newton’s Method	1, 3, 4, 31 7, 8, 11, 13, 15, 18, 19, 21, 23, 36
4.9	Finding antiderivatives (Know the basic examples in the table on page 341.) Arbitrary constant Analyzing motion	1-6, 9, 11, 12, 14, 15, 18, 23-28, 49-51, 53, 55-56 21, 29-32, 39 57, 58, 59, 61
5.1	Approximating area by rectangles Riemann sums Improving approximations by a limit Distance and velocity problems	1, 4a, 5 13 19, 23, 24 11, 12, 15
5.2	Concept of definite integral Notation for the definite integral Basic properties (pages 373 and 375)	1, 5a, 21, 23, 27, 33, 35, 36, 37, 39 17, 18 41, 42, 43, 52
5.3	Area function Fundamental Theorem, part 1: derivative of the area function equals the integrand. Fundamental Theorem, part 2: value of an integral equals a calculation with an antiderivative	2, 5, 52, 63 5, 7, 8, 9, 11, 12 19, 20, 21, 23, 25, 26, 27, 28, 30, 31, 32, 35, 38, 39

You will also be expected to be comfortable doing the following in Maple:

basic arithmetic, simplifying an expression, creating a function, evaluating a function, plotting a function, taking a limit, finding a derivative, calculating Newton’s Method, finding an antiderivative, calculating a definite integral

Here are some major topics from the earlier chapters. You should refer to the study guides from our previous tests.

Chapter 1: Functions and Models

Functions in general: domain, range, symmetry. This includes polynomial, rational , and trig functions.
Linear functions: finding slope, creating equations of lines
Composition
Exponential laws and exponential functions
Inverse functions
Logarithm laws and logarithmic functions

Chapter 2: Limits and Derivatives

Tangent lines
Average Velocity
Calculating limits, including left and right limits, and as x goes to infinity
Continuous functions, and how continuity can fail
Finding asymptotes
Derivative = limit of a difference quotient
Derivative = rate of change. This includes velocity = rate of change for position.
Derivative can be used to calculate slope.
How a function can fail to be differentiable.

Chapter 3: Differentiation Rules

Calculating derivatives: basic rules, trig rules, exponential and log rules
Product Rule, Quotient Rule, and especially the Chain Rule
Derivatives of implicit functions
Applications involving rate of change
Growth and decay by exponential functions

Chapter 4: Applications of Differentiation

Absolute maximums and minimums; local extrema or endpoints
Increasing versus decreasing, and the first derivative
Concavity and the second derivative
Indeterminate forms and L’Hopital’s Rule
Graphing with calculus

MATH 117 Section FG Topics for Final Exam

MATH 117 Section FG
Topics for Final Exam