MAT137Y5 Study Guide - Quiz Guide: Scilab, Limit Comparison Test, Improper IntegralExam
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MAT 137Y - TERM TEST 4 REVIEW SHEET PAGE 1OF 4MAT 137Y - TERM TEST 4 REVIEW SHEET PAGE 1OF 4MAT 137Y - TERM TEST 4 REVIEW SHEET PAGE 1OF 4
•The test is 1.10 →2.50 on Friday, March 22, 2019, in KN 137. Please arrive about 5 minutes
early, so that we can start on time.
•Please learn your tutorial information. Tests are returned in tutorial.
There will be a 2 point penalty for missing or incorrect tutorial information.
•There are no calculators, notes or books allowed.
•The test will have 5 questions: 40% is computation, 40% is proof/conceptual, 20% True/False.
•Remember to bring your TCard to the test. (We will be taking attendance for the test!)
•Oﬃce hours for the week of the test are as follows:
Instructor/TA Time Place
Esentepe TBA DH 3097-A
Bibilo TBA DH 3064
Thind TBA DH 3025
David TBA DH 2027
Jayde TBA DH 2027
Rodney TBA DH 2027
•The test covers material from class, HW, quizzes and practice problems related to: 6.1, 6.2,
6.3, 6.4, 6.5, 7.1, 7.4, 7.5, 7.8, 7.9, 8.1, 8.2
•Here is a summary of topics you should know for the exam. It is meant to be a guide for
your own studying. It is your responsibility to do a thorough review of your own notes from
class, HW and TUT problems, and to go over the related material from the textbook. So use
this list as a guide, but make sure you are comfortable with the practice problems, tutorial
problems and the material and examples covered in lecture.
Things to know for the test
•Previous Material - You should know the previous material, and be able to use it to solve
new problems. In particular: You should still remember all your basic antiderivatives. You
must know the antiderivatives of the following basic functions: xn,ex, sin x, cos x,1
√1−x2, sec2x, sec xtan x. You should know how to take limits. You should be able to factor
and solve equations. However, you will not be tested explicitly on the material from Test 1,
Test 2, or Test 3.
•Substitutions - You should understand that the “substitution method” is really just chain
rule in reverse. You should know how substitutions work, and be able to recognize when it
might be a good idea to try one. (Hint: Look for a composition, look for a product.) Don’t
forget to “substitute back” so that your ﬁnal answer has the same variable as the questions
asked. When using substitutions for deﬁnite integrals, don’t forget that the bounds of inte-
gration change too.
•Integration by Parts - You should how, and when, to use integration by parts. Be careful,
sometimes you have to use it more than once to get the right answer, and sometimes you might
need a substitution before or after using integration by parts to get the right answer.
•Trig Integrals - You should know the strategy for integrating powers of sin,cos, and tan,sec.
You will need to know sin2x+ cos2x= 1 and tan2x+ 1 = sec2x, but you will be given the
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