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# Short Calculus MAT 016A

UCD

GPA 3.88

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This 2 page Class Notes was uploaded by Otilia Murray I on Tuesday September 8, 2015. The Class Notes belongs to MAT 016A at University of California - Davis taught by Hillel Raz in Fall. Since its upload, it has received 61 views. For similar materials see /class/187386/mat-016a-university-of-california-davis in Mathematics (M) at University of California - Davis.

## Reviews for Short Calculus

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Date Created: 09/08/15

This is a review sheet for the second midterm in Hillells MAT 16A It is a list of the topics that will be covered on the exam along with sample questions The exam itself will not be this long Some of the questions on it though will be very similar to questions on this review sheet andor the homework Good luck studyingl Chapter 2 0 Sections 24 27 84 Know how to take derivatives using the product rule the quotient rule and the chain rule 2425 It might be wise to simply ask yourself which rule you should use before using it just to think about the problem rst Know how to take derivatives of trigonometric functions 84 you should also know the different trig functions and their values on the unit circle as we did in class 8183 Know how take the second third fourthw derivatives of different functions 26 Know how to take the implicit derivative of a function 27 Sample problems 1 For the following nd their derivatives a 315 717z4 71812 29 b cosz sinz tanz cscz o m733Qg3 o m7wamp 4x5 7 31 72 d 51 l e cot31 1 You could nd many more examples in the book homework class notes etc 2 For the following nd f z and f30 awm7mm b m W 11 3 Solve for d7 a y2 13 81 b SIyQ 151 5 c 2z2y4 7 53 8 0 Sections 23 28 Applications Know the difference between average rate of change and instantaneous rate of change 23 Given a position or height function know how to nd the velocity andor acceleration functions 23 now how to solve word problems with related rates 28 Sample problems 4 Find the average of change of 21 J 7 on 0 2 and on 5 1i z 5 A diver jumps from a diving board that is 64 feet high She jump up with an initial velocity of 48 feet a second Use that information to write the height function h 716t2 vot her Then calculate the time she hits the water and her velocity and acceleration at that time 6 A 30 foot ladder is leaning against a house The base of the ladder is pulled away from the house at a rate of 4 feet a second How fast is the top of the ladder moving down when the base is 8 feet away There are many more related rates andor velocitymarignals questions in the book You are responsible for those that were covered in class or in the homework If we didn t cover them you are not responsible for themi Make sure though you get enough practice doing these You can also look in the chapter review p 166169 Chapter 3 Sections 3132 Know what it means for a function to be increasing or decreasing 3 1 now how to nd the intervals where a function is increasing or de creasing 3 1 Know the difference between relative and absolute extrema 3 2 Know how to nd extrema and how to classify them as relativeabsolute maxmin 3 2 now the extreme value theorem 3 2 7 For the following functions nd the intervals on which they are increas ing or decreasing and label them as such a ET 7 41 b 12 7 945 on 4 5 watch out for the unde ned part c 2cosz on 0270 8 For the functions above nd their relative maxmin and absolute maxmini

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