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# Calculus I MATH 115

UM

GPA 3.87

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This 1 page Class Notes was uploaded by Mrs. Preston Lehner on Thursday October 29, 2015. The Class Notes belongs to MATH 115 at University of Michigan taught by Staff in Fall. Since its upload, it has received 10 views. For similar materials see /class/231499/math-115-university-of-michigan in Mathematics (M) at University of Michigan.

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Date Created: 10/29/15

Math 115 Review Sheet for Exam II This exam covers Chapters 2 and 4 and Sections 51 and 52 Although this exam is not cumulative in the usual sense since there will be no questions whose only purpose is to test your knowledge of Chapter 1 and Appendix A it is still the case that you must be familiar with the material from those earlier portions of the book since much of this newer material depends upon it As with the review sheet for the first exam you should not assume that a topic will not be on the exam just because it is not mentioned on this sheet All of the material in the sections mentioned above is fair game General Topics anal Skills You should understand the concept of a rate of change in its different forms and in particular know the difference between average and instantaneous rates of change You should be familiar with the term derivative and understand that it measures the instantaneous rate of change of a function You should be able to compute and represent rates of change algebraically using formulas numerically and graphically You should understand and be able to discuss the practical meaning and applications of a rate of change You should understand the information that the signs of the first and second derivatives give you You should understand the difference between an approximate answer and an exact answer and know which methods give which Speci c Topics anal Skills by Section You should know the difference between average and instantaneous velocity You should be able to compute or estimate average and instantaneous velocity if you know position as a function of time You should understand that instantaneous velocity is a limit of average velocities You should understand the meaning of the limit notation and be able to work with it You should know the meaning of derivative tangent line and instantaneous rate of change You should be able to estimate derivatives numerically using a table or graphically by approximating the slope of a tangent line You should understand how to find the equation of a tangent line if you know the derivative Given the graph of a function f you should be able to sketch a graph of f 39 Similarly given the graph of a function g you should be able to sketch a function f such that f 39 g You should understand how the sign of the derivative relates to whether or not the function is increasing or decreasing You should be able to explain in ordinary English the practical meaning of a derivative of a function that models a realworld situation You should understand

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