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# CALCULUS WITH FUNCTIONS I [C3T1G1] MATH 231

JMU

GPA 3.61

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This 3 page Study Guide was uploaded by Eunice Schoen on Saturday September 26, 2015. The Study Guide belongs to MATH 231 at James Madison University taught by Staff in Fall. Since its upload, it has received 15 views. For similar materials see /class/214037/math-231-james-madison-university in Mathematics (M) at James Madison University.

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Date Created: 09/26/15

Math 231 Exam 1 Review Exam 1 will be entirely inclassi l7m planning for it to take up most of the alloted time maybe 50 minutes so that you will have some time to check your wor The midterm will consist of three separate parts The rst part will be de nitions all taken from the list below The second part will be simple problems designed to be straitforward applications of the basic concepts each should take under ve minutes The goal of these parts is to make sure that you understand enough to fol low along in lecture Expect this part to be like easyish homework problems The third part will be comparable to the more theoretical homework problems Expect the problems from the third part to be like mediumhard homework problems De nitions will be taken from the following list The indicates de nitions which might be completely new to you Sets and numbers Multiplication for whole numbers it is repeated addition but for nonwhole numbers it s i the area of the rectangle with side lengths lal and Set a collection of objects called elements Set notation be able to read for example I l I 2 l and z E A ZQlab Zandb7 0R lrrational number formal de ntion I f for my a b E Z Interval notation open and closed intervals open and closed rays Venn diagram this will not be in the de nitions portion of the exam but you may be asked to draw a Venn absolute value both the formal de nition on p 9 and the informal distance from 0 de nition diagram in the problems section of the exam so know what one is Cartesian plane Equations Equation Solution to an equation Factoring Which theorem is the reason factoring helps solve equations A B 0 if and only if either A 0 or B 0 Which formula do we use to solve the quadratic equation az2 121 c 0 for any a b and c Quadratic formula I ibi W Inequalities Theorem the sign of a product depends on the sign of its factorsi lnequalities and absolute values be able to translate an absolute value of the form lz 7 cl lt 6 into words ie the distance between I and c is less than 6 and visa versa Triangle inequality Absolute value of a product is the product of the absolute values Logic V be able to translate it into works and use it in a sentence 3 same as above Negation of a logical statement Logical connectors 77and77 and 77or77 be able to give their truth tables and negations Counterexample implies also be able to give its truth table 42gt if and only if be able to give its truth table Contrapositive of A B be able to show A B is equivalent to its contrapositive either using truth tables or in words Converse of A B which is B A also note that knowing A B is true tells you exactly nothing about its coverse B Proofs Direct proof Proof by contradition Functions Function also know functional notation like f z A A B and y omain Target Math 231 Extra Problems Exam 2 Material DISCLAIMER This is not to substitute study of the assigned HW problems quizzes lecture notes etc You should still look over in class examples and any problems you were assigned These are extra practice problems for you over and above the assigned HWl In fact I recommend you study the HW problems rst and then look at these extra problemsl Also all the quizzes l have given to both of my 231 classes are on Blackboard I strongly recommend you look at those quizzes even if you didn t take it ie the other class took the quiz and you turned in H E0 9 F 5 Evaluate the following limits if they exist 2 7 2 a 1111132 ltbgt 2 0 310 d 1211 I 7 1 7r I2 7 1 Compute the derivatives the following functions a ln10 65M z b 93 583 7 i c vt tt 7 2 d fW 632 99 e 9A i 33 Use the de nition of continuity to determine if is continuous at z 3 where 11 ifzlt3 fz 2 ifz3 279 ifzgt3 Suppose if z rational 2 7 12 ms 7 4 a Use the de nition of continuity to determine if is continuous at z 2 b Use the de nition of the derivative to determine if is differentiable at z 2 if z irrational Let Find an equation of the tangent line to at the point 273 i Let 13 7 31 1 Show there is some point c such that 2 Be sure to state any theorems or properties that you use and how they apply Math 231 Exam 2 Review l7m planning for the exam to take up most of the alloted time maybe 55 minutes so that you will have some time to check your wor The problems on the midterm will fall into roughly three catigories The rst is de nitionstheorems all taken from the list below You will be asked to state de nitions or theorems and possibly provide examples Notice that most of your quizes have had a problem like this The second type of problem will be simple problems designed to be straitforward applications of the basic concepts each should take under ve minutes The goal of these parts is to make sure that you understand enough to follow along in lecture Expect this part to be like easyish homework problems The third type will be comparable to the more theoretical homework problems Expect the problems from the third part to be like mediumhard homework problems I will try to provide examples of type 2 and 3 problems from your assigned homework for each section as well as pointing out problems that I would consider to be too hard to put on the exam To study for this exam I suggest 1 Read through the book and your class notes Include the example problems in each section of the book This exam covers sections 31 through 42 though I will assume you know the material from the previous chapters 2 Write down the de nitionstheorems on the list below A few of them are very nicky de ntions that it is probabily better to learn word for word from the book but most have multiple ways to state them correctly 3 o homework problems If you think that you understand all of the homework problems that were assigned try testing your knowledge with similar problems whose answers are in the back of the book If you do not know how to do a particular homework problem before asking someone else how to do it try to nd a similar problem that was done in an example in that section Also try one of the earlier problems in that section that has an answer in the back of the book If all else fails at least write down the relevant de nitions for that problem Then go nd help The MathScience Help Center is open on Sunday afternoon and all day on Monday You can email me over the weekend Also working on problems with other students can be very bene cial to all involved 4 GET AT LEAST 8 HOURS OF SLEEP ON MONDAY NIGHT If it comes down to a choice between studying for this exam and sleeping SLEEP Your capacity for logical deduction is your most important tool for a math test and if you havenlt slept it is very hard to think De nitionstheorems will be taken from the following list indicates de nitions which might be completely new to you the 11 indicates de nitions that have precise statements so care needs to be taken with them Tangent lines and the derivative at a poi t Tangent line to at z c also an informal description of it Secant line Slope of the tangent and how it relates to the slope of secant lines 41 Derivative of a function at a point 41 Alternative de nition of derivative of a function at a point 41 Left and right derivatives relevant homework problems from this section all except 1675 would also change 212430 to noncalculator problems Derivative as an instantaneous rate of change Average velocityrate of change lnstantaneous velocityrate of change Acceleration and how it relates to the velocity function Graphical interpretations of both average velocity and instantaneous velocity relevant homework problems from this section all of them Differentiability Differentiability at a point 41 Differentiable function Differentiability implies continuity relevant homework problems from this section all of them Derivative as a function 41 Derivative function 41 Alternative de nition of the derivative function Derivative notation know at least fz fz 2 f clC and Higher order derivatives and their two notations Second derivative of a position function is acceleration

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