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Calculus I

by: Breanne Schaden PhD

Calculus I MATH 170

Breanne Schaden PhD
GPA 3.72

Melvin Holmes

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Melvin Holmes
Class Notes
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This 4 page Class Notes was uploaded by Breanne Schaden PhD on Saturday October 3, 2015. The Class Notes belongs to MATH 170 at Boise State University taught by Melvin Holmes in Fall. Since its upload, it has received 15 views. For similar materials see /class/217992/math-170-boise-state-university in Mathematics (M) at Boise State University.

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Date Created: 10/03/15
Topics for Review for Final Exam Dr Holmes May 3 2005 The exam will be open book scienti c calculators only no graphing or symbolic computation capability I misguided when I said on Monday that fancy calculators would be allowed The material will be fairly evenly distributed through the book except for the necessity of covering sections 55 and 56 In general questions on this exam will look like questions on the hour exams but this does not mean that each question on the nal will be exactly similar to some question on one of the hour exams There will probably be one word problem on the exam though two is not out of the question you will have a choice of problems to do Nothing I say in this document in any way restricts what I may ask on the hardest question on the exam The remainder of this document discusses coverage of material from spe ci c chapters in the book section 21 Questions testing your understanding of the tangent and ve locity problem asking you to compare secant lines or average velocities with tangent lines or instantaneous velocities may be expected sections 22 23 You need to know the basic properties of limits and be able to use the limit laws to reason about them I may ask questions involving piecewise de ned functions to test your understanding of lim its from the left and the right A related topic from later in the book is L Hopital s Rule section 24 If I ask a question about the formal de nition of limit it will be similar to the question I asked on the rst exam Be sure that you write out the de nition correctly section 25 Understand the definition of continuity and be prepared to answer a question requiring you to verify continuity of a function at a point using the definition Classification of discontinuities might show up section 26 Topics in this section will be subsumed under curve sketching though limits at infinity or infinite limits might show up in a general limit question sections 27 29 Be prepared to compute a simple derivative directly from the definition using limits Also be able to compute tangent lines to curves at points sections 31 32 Be able to compute derivatives Since we will not be using fancy calculators you may expect to be tested on computation of derivatives by hand Questions which test your understanding of the rules without giving you an explicit formula for a function such 32 problems 35 or 36 are possible section 34 Know the derivatives of the trig functions including tangent and secant I don t plan to ask about details of proofs in this section section 35 Same remarks for 31 and 32 I may ask questions testing your ability to set up chain rule problems using the Leibniz notation Look at problems 57 and 58 section 36 Be able to do implicit differentiation and to find tangent lines to curves defined implicitly Be able to use implicit differentiation to find the derivative of the inverse of a function we did for the inverse trig functions and the logarithm section 37 Be able to read the notation for higher derivatives and compute them section 38 Be able to compute derivatives of functions involving the loga rithm Be able to compute derivatives using logarithmic differentiation section 310 I might ask a related rates question but it is more likely that you will have a choice of maxmin problems sections 478 section 311 No coverage of this section is intended section 41 Be able to nd absolute maxima and minima of continuous functions on closed intervals But this might not show up maxmin questions naturally fold into curve sketching section 42 I m not likely to ask about the Mean Value Theorem on this exam sections 43 45 Be prepared to do curve sketching questions like the questions on Test 3 or 4 or like problems 26 30 in section 43 Be sure to give all the details I ask for section 44 Be able to compute limits using L Hopital s Rule and be sure you know when the rule applies and when it doesn t You are allowed to use L Hopital s Rule in a general limit question even ifI don t mention it in the instructions and I might not unless I speci cally tell you that you can t use it sections 47 48 There will be max min word problems You will be asked to do one or two word problems from a list which might include one or more 310 problems well section 49 I m inclined not to ask about this section 410 Be able to compute antiderivatives You will not escape this time from a problem like problem 6 on Test IV and it is possible that this problem on the test will allow you to make up problem 6 Test IV though I have made no nal decision about this section 51 A question like the one on Test IV where you are called upon to compute a speci c sum of areas of rectangles to approximate an integral and sketch the rectangles This is the only kind of 51 question I will ask of course I might ask a velocity problem question instead estimate displacement of an object with a given velocity function over a given interval of time the math would be the same though section 52 Be aware of the basic properties of integrals discussed in this section No fancy limits of summations section 53 No FTC part 1 just evaluation of de nite integrals using the fundamental theorem section 54 I might ask a question contrasting displacement and total dis tance travelled for a moving particle problems 53 56 are good to look at section 55 Be able to compute antiderivatives and de nite integrals using substitution You may use either approch to de nite integrals Know how to integrate the tangent function section 56 No questions specifically about this section you should already know that the antiderivative of is ln t it s possible that I might ask some kind of question which looks like it is motivated by ideas in this section but knowledge from earlier sections will be enough to do the problem


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