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Review Guide for MAT220 Midterm Exam Part I. Fall 2016.
Part 1 is worth 50% of your Midterm Exam grade. Syllabus approved calculators are okay to use on this part of the exam
(but not necessary). All work will be done on the test itself; you may NOT use any scratch paper. Partial credit WILL be
awarded for partially correct work so be sure to show ALL of your steps. Correct answers without the correct
corresponding work are worth nothing.
Note: Section numbers have been provided by each topic so that you can go back through your NOTES, HOMEWORK
and OLD TESTS to find problems to practice. You can also go back to the class HELP page and view some of the relevant
supplemental readings and videos.
A. Be able to evaluate a limit using conjugation (section 1.2).
Lim
x 2
x2
x  11  3
B. Be able to evaluate a limit involving trigonometric functions (section 1.2). May involve factoring and/or properties of
functions. Special trig limits may be involved in part of it.
Lim
x0
sin x  sin 2 x
x
C. Given a piecewise defined function be able to determine if it is continuous at a specific x-value. Also be able to
determine if it is differentiable at a specific x-value (section 1.3 and section 1.5)
 x2  x
h  x  
sin x
x0
x0
Is this function continuous at x = 0? Explain. Is this function differentiable at x = 0? Explain.
D. Be able to use the limit definition of derivative to find the derivative of a polynomial function. Also be able to use the
alternate limit definition to find the value of the derivative of a function at a specific point. In fact you should also
practice finding the equation of a tangent line to a function at a given point (section 1.5).
Use the limit definition of derivative or the alternate limit definition of derivative (is one of them easier to use here?) to help you find
the equation of the tangent line to the graph of the function f  x   3 x  4 x  5
2
at
1, 4 
E. Be able to find the derivative of a variety of different types of functions using the differentiation rules that we
developed in this course. For example, make sure you can find derivatives for exponential functions ( e u ), various
trigonometric functions, logarithmic functions and inverse trigonometric functions. Also practice finding derivatives of
products(product rule), quotients (quotient rule) and compositions (chain rule) of these types of functions (sections 1.6,
2.1, 2.2, 2.4). There will be multiple problems for you to demonstrate your competency on this skill. Remember to
always leave your answers in simplified factored form. NOTE: find the derivative for each function below WITHOUT
rewriting it first!
g  x   e 4 x cos 2 x
y  ln  sin 3  4 x  
f  x 
cot x
csc x
h  x   arccos  4 x 
F. Be sure that you can use implicit differentiation to find y  when given an equation (section 2.3). Make sure that you
“simplify” your final answer just like I did in your class notes and in the homework solutions!
x 3  4 ln y  y 4  7
G. Be sure that you can use logarithmic differentiation to find y  when given an equation (section 2.3). Make sure that
you “simplify” your final answer just like I did in your class notes and in the homework solutions!
y  x4 x2 1
NOTE: The sample problems provided here are NOT intended to be the only problems that you look at while preparing
for this Midterm exam. Be sure to READ the information provided after each alphabetic letter above and spend time
searching your old tests, notes and homework to review the mentioned topics. Make sure that you understand the
mathematics relevant to each topic NOT just how to do a set of particular problems!
It is unlikely that you will finish this test in the given amount of time unless you are EXCEPTIONALLY well prepared. You
have only 65 minutes to complete as much as you can. This test may prove to be very challenging unless you have taken
the necessary steps throughout the semester to learn all of the material we covered.