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Short Calculus

by: Otilia Murray I

Short Calculus MAT 016A

Otilia Murray I
GPA 3.88

Hillel Raz

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Hillel Raz
Study Guide
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This 2 page Study Guide was uploaded by Otilia Murray I on Tuesday September 8, 2015. The Study Guide belongs to MAT 016A at University of California - Davis taught by Hillel Raz in Fall. Since its upload, it has received 95 views. For similar materials see /class/187386/mat-016a-university-of-california-davis in Mathematics (M) at University of California - Davis.

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Popular in Mathematics (M)


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Date Created: 09/08/15
The following is a study guide It lists the topics that will de nitely be on the nal and those that a few questions will be selected from You can look at it as one of those travel guides that gives you a plan according to the amount of time you have to spend in a city or a region if you have 3 hours to study de nitely review those topics that will be on the nal If you have 6 hours to study in addition to those topics mentioned above review the concepts that could be on the nal If you have 10 or more hours to study do practice problems from the chapter reviews review your old midterms and the practice midterms and the examples done in class and if possible your homeworks Most of the questions on the nal will be questions you have already seen changed a bit You should also know the basic theorems derivative tests and de nitions that we learned in class Good luck 0 Topics that will DEFINITELY be covered on the nal ote that some of these will be covered directly in questions while others will be parts of other questions Functions and their domains 14 Limits what are they their properties nding them 15 The slope of a graph and the de nition of a derivative and how to nd the derivative of a function using the de nition of the derivative using the limit h A 0 1 Derivatives and all the different rules product rule quotient rule chain rule 22 24 25 Using derivatives to answer application questions such as velocityacceleration or rates of change 23 28 Trigonometric functions and their properties including their deriva tives In particular values of the trig functions on the unit circle SJ84 Finding critical points of functions in order to nd intervals on which the function is increasing or decreasing 31 Finding maximum and minimum points 32 Finding the points of in ection of a function and the intervals on which its concave up or down 33 Using the second derivative test to nd if a point is a maximum or a minimum 33 Sketching a curve by analyzing its domain its extrema points the intervals on which its increasingdecreasingconcave upconcave down and its in ection points 37 Optimization problems 34 35 Finding differentials of functions 38 0 From the following list a few topics will be covered though not all of them will be on the nal for certain Topics that could be covered on the Final The distance formula 11 Writing the equation of a circle and graphing a circle correctly 12 Onesided limits 15 De nition of continuity 16 Average rate of change 23 Marginals 23 Implicit differentiation 27 note that implicit differentiation is an extremely important part of rates of change problems and will be covered through those The difference between relative extrema and absolute extrema 3 2 Asymptotes will be covered through section 37 direct questions such as in section 36 may or may not appear For possible questions look at old midterms and practice midterms class notes and homeworksi For practice you can do the chapter review questions on the subject or other problems in the book Here are sample questions that we hadnt covered yet on any midterm sec tions 3335 37 3 8 1 Identify all relative extrema and points of in ection for the following as well as intervals of concavity many more problems like these in section 33 or 84 a 13 7121 b fltzgt I 1 c 123 7 3 d y 2sinz cos21 2 Analyze the functions above and graph themi 3 The difference of two numbers is 50 Find the two numbers such that their product is a minimumi What if the they both have to be positive 4 Find the point on the line 213y5 0 that is closest to the point 1 2i There are many more such problems in section 34 and in the chapter review 5 Find the differential dy of the following a y 12 17 5178 b 7 y 9 cy6z4751318 6 For 5a above nd the value of dy when I 2 and dz 001i


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