10B_REVIEW

10B_REVIEW - Math 10B Final Exam Review Outline Basic...

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1 Math 10B Final Exam Review Outline Basic Information for the Final Exam: The final will consist of approximately 8-9 questions . The final exam will be cumulative ; it will not focus too much on any particular topic. Most likely, the recent material will have more emphasis than the older material. However, in a math class, it all builds upon itself. You will be allowed a calculator on the exam, so please bring one. There is no restriction on what you can bring, but you will not need anything more powerful than a TI-83. (You can probably get away with just a TI-34 or no calculator, actually.) You should bring a number two pencil. (You can bring more than one if you feel so inclined.) You are permitted a handwritten reference sheet on the exam (8.5 x 11 inches). You can put whatever you feel is important on it (see the rest of this document for ideas.) Please, do not bring anything more than this. We reserve the right to place your backpacks in the front of the class. You don’t need to worry about bringing a blue book, as you will be able to write directly on the exam. The exam will be held Wednesday, March 21 st , 2006 from 7:00 – 10:00pm , in the following rooms: The test is designed to take about two hours. This means that you should have sufficient time to go back through your work and check your math. Remember, does your answer make sense? (Draw a picture/plug numbers in.) Solutions will be posted on the Math 10B website http://math.ucsd.edu/~jeggers/math10b/ some time after the exam so you can get a rough idea how you did. (Solutions should be up by Tuesday morning, if not sooner.) I have included a reference sheet for the material from the course. Most formulas have been included. You can look over this, but you will not be allowed to use it on the exam. (You are allowed to bring a handwritten page of notes.) Lecture/Time Room Eggers/9am ?? Hohnhold/8am ?? Berg/4pm ?? Bell/2pm ??
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Formula Sheet for Math 10B – Final Exam Common Integrals : 1 . adx ax C =+ , a constant. 2 . 1 1 n n ax n ax dx C + + , 1 n ≠− 3 . 1 ln x ad x a x C 4 . 11 ln ax b a dx ax b C + + 5 . 1 ax ax a ed x e C = + 6 . ( ) 2 1 1 arctan x dx x C + = + 7 . 1 cos( ) sin( ) a ax dx ax C = + 8 . 1 sin( ) cos( ) a ax dx ax C = −+ First Fundamental Theorem of Calculus : “If f is continuous on [ a , b ] and f ( t ) = F ( t ), then () b a ftd t = F ( b ) – F ( a ).” Second Fundamental Theorem of Calculus : “If f is continuous on an interval and a is any number in that interval, then the function F is defined as follows is an antiderivative of f : x a Fx t =∫ .” Average value of f from a to b : 1 b a ba f xdx Properties of integrals : 1 . ab ∫= 2. cbb ac a ∫+ 3. bb b aa a f xg x d x f x d x g x d x ∫± = ± 4. cf x dx c f x dx 5. If f ( x ) g ( x ) for a x b , t h e n gxdx ∫≤ Deriv/Int of Sin/Cos : Equations of Motion : 2 00 1 2 st g t vt s =− + + , v 0 , initial velocity, s 0 initial position, g is gravity (either 32 ft/sec 2 or 9.8 m/sec 2 .) Integration By Substitution : (() ) () ) f gx g xd x f gx C ′′ If you see a function inside of another function (typically with parentheses), let the inside function be
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10B_REVIEW - Math 10B Final Exam Review Outline Basic...

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