Here is a review for your upcoming test. The
test covers sections 1.1 through
3.3. I will not collect this. Do what you want with it.
will give you a good indication of what you will be expected to know
test. Obviously, this review is
longer than the exam will be. In a
few days, I will post partial solutions to the questions in Part II.
Here is a list of things that absolutely must know
- Shapes of basic graphs
- Find domain
- Combine functions together (sum, difference,
product, quotient, composition) and find domain
- Find slope
- Find equation of line passing through 2 given
- Find equation of line parallel/perpendicular to
a given line and passing through a given point
- Limit Laws
- Evaluate limits (both sides, from the left, and
from the right)
- Squeeze Law
- Intermediate Value Theorem
- Limit definition of derivative
- Find slope of tangent line to a given function
at a given point
- Find equation of tangent line to a graph at a
- Power rule
- Product rule
- Quotient rule
- Chain rule
During the exam, SHOW ALL YOUR WORK and
JUSTIFY YOUR ANSWERS when necessary.
Also, be organized and neat!
Don’t forget to write limits where you need them. Also, don’t
forget to ask yourself if
you need to rewrite a function before finding the derivative.
And, if you rewrite a function before
finding the derivative, do not label the function as the derivative.
Part I: Give
answer to each of the following.
- When you are trying to find the domain of a
function, what are the two major things that you need to think about
- Given functions
, how to you find the domain
- What is the first thing that you should do when
evaluating limits? What are the three possibilities and what do
you do in each case?
- When doing limits involving trig functions,
what is the theorem that you want to try to use?
- When using the Squeeze Law, how do you go about
picking the “top” and “bottom” functions? What work do you need
- What would a question look like that would
require you to use the IVT? What are the hypotheses that you need
to satisfy to use the IVT?
- What is the limit definition of the
derivative? What the heck is the derivative?
- Think of some examples where it’s a good idea
to rewrite the equation before finding the derivative.
- When do you need to use the product rule?
Quotient rule? Chain rule?
- How do you find the equation of the tangent
line to a graph at a given point?
Part II: Answer
of the following questions.
- Exercise #19, page 49
- Exercise #23, page 49
- Exercise #6, page 32
- Use limit laws to evaluate:
- Evaluate the following limits if they exist.
Exercise #27, page 85
Is the following function continuous for all real
numbers? Why or why not?
Prove that the following function has at least one zero in the
Find all vertical asymptotes of the following function.
Explain why the limit as x
approaches 0 of the following function does not exist.
Use the limit definition to find the derivative of the
does not exist.
Differentiate each of the following functions, but do not
- Find an equation of the tangent line to the