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Short Calculus

by: Otilia Murray I

Short Calculus MAT 016A

Otilia Murray I
GPA 3.88


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Class Notes
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This 4 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 Staff in Fall. Since its upload, it has received 25 views. For similar materials see /class/187459/mat-016a-university-of-california-davis in Mathematics (M) at University of California - Davis.

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Date Created: 09/08/15
Review Sheet for 16A3 nal Thomases W09 Here is a list of the sections and topics we have covered though not in the order we covered them on the nal everything is fair game 0 Chapter 1 11 16 topics include distance formula completing the square graphs of simple equations circles lines parabolas functions de nitions domain range one to one inverse functions limits continuity Chapter 2 21 28 topics include de nition of the derivative derivative as slope of tangent line differentiation rules sum rule constant multiple rule product rule quotient rule chain rule derivative as rate of change velocity and acceleration higher order differentiation second derivatives and such implicit differentiation related rate problems Chapter 3 31 34 36 37 38 topics include increasing and decreasing functions the rst derivative test concavity and the second derivative test local and global extrema optimization problems maxmin problems asymptotes related to limits and useful for graphing curve sketching linear approximation and differentials Chapter 8 81 84 topics include radian and degree conversion for trigonometry the trigonometric functions graphs of trigonometric functions derivatives of trigonometric functions To practice for the nal 1 suggest you study the following 0 Practice problems included here note that these problems only cover the material since the second midterm namely 27 28 34 38 0 Practice problems for midterms 1 and 2 solutions available online 0 Midterms 1 and 2 solutions available online 0 All previous quizzes solutions available online 0 Read through examples in course notes available online 0 All homework problems Outline The nal will have a distribution of problems approximately as described below This list is only approximate and to prepare well for the exam you must study all of the topics we have covered in the class Don t forget that any of the problems below could include trigonometric functions so make sure to study the trig functions their derivatives and remember how to evaluate them at the familiar values 7T6 7T4 7T3 etc o 1 3 limits 0 1 question about continuity o 1 3 derivatives may include implicit differentiation or higher derivatives 0 1 limit de nition of the derivative 0 1 tangent line or related problem may involve implicit differentiation 0 1 detailed graphing problem involving nding domain7 critical points7 local extrema7 concavity7 limits at 00 vertical asymptotes7 etc o 2 4 word problems related rates7 maxmin7 linear approximation 0 1 velocityacceleration problem gravity 1 will give you the formula ht 16t2vot ho or bug77 problem 0 1 rst derivative test or concavity problem 0 2 additional problems Here is a list of the formulas you will be given on the test in addition if you need any geometric formulas for max min or related rates problems you will be given those as well sin26cos26 1 sin26 2sin6cos6 tan2 6 1 sec2 6 cos 26 cos2 6 7 sin2 6 1cot26csc26 cos262cos2671 cos26172sin26 Here are the practice problems solutions will be available by Friday 1 Find 2 by implicit differentiation a x2iccyy38 b x2l my c cosa i y ysina 2 Find an equation of the tangent line to the curve at the given point 22 2 a E i 9 l at the pomt 75 b y2 5532 733 at 11 9quot Car A is traveling west at 50 miles per hour and car B is traveling north at 60 miles per hour Both are headed for the intersection of the two roads At what rate are the cars approaching each other when car A is 03 miles and car B is 04 miles from the intersection r A baseball diamond is a square with side 90 feet A batter hits the ball and runs toward rst base with a speed of 24 feet per second At what rate is his distance from second base decreasing when he is halfway to rst base7 See gure 1 Second base Third base Firstbase 90 feet Homeplate Figure 1 problem 4 5 Find the point on the parabola y2 233 that is closest to the point 14 6 Find two numbers whose difference is 100 and whose product is a minimum 7 Approximate 5801 8 Compare the values of Ag and dy if y x3 2 7 2x 1 as x Changes from 2 to 205


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