MTH 150 Final Exam Review

MTH 150 Final Exam Review - MTH 150 FINAL EXAM PREPARATION...

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MTH 150 FINAL EXAM PREPARATION DATE & TIME: _____________________________________________________________ FORMAT: 45 multiple choice problems BRING: TI-83/84 calculator, #2 pencils, a good eraser STUDY: chapter reviews, chapter exams, final exam review IMPORTANT TOPICS: Finding limits, derivatives, and integrals make up the foundation of your study of calculus, but be sure to also study the following theorems, applications, and graphical concepts. Theorems and Definitions h Formal Definition of a Limit (2.2) h Intermediate Value Theorem (2.4) h Limit Definition of a Derivative (3.1) h Extreme Value Theorem (4.1) h Rolle’s Theorem / Mean Value Theorem (4.2) h Limit Definition of Definite Integral (5.3) h MVT for Integrals (5.4) Applications h Linear Motion (3.2, 3.3, 5.1) h Related Rates (3.7) h Newton’s Method (3.8) h Optimization (4.7) h Error Propagation (4.8) h Area (5.2) Graphical Concepts h Determine limits graphically h f and the slope/direction of f h f ′′ and the concavity of f h Definite integral and area

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MTH 150 Final Exam Review Limits (Chapter 2) 1. Find the limits: a. 2 1 2 lim 1 x x x x + - - - f. 0 lim tan x x x b. 2 1 1 2 1 lim 1 x x x - - - g. ( ) ( ) 0 sin 4 lim cos 3 θ c. 3 3 lim 3 x x x - - h. ( ) 2/ 0 1 cos lim 1 t t t t t - + + d. ( ) 1 lim x f x if ( ) 3 , 1 1, 1 x x f x x - = = i. sin lim x x x →∞ e. 2 2 2 lim 4 x x x - - j. 2 2 1 4 lim 5 13 x x x x →∞ - - + 2. For which of the following functions f (if any) does ( ) 1 lim x f x fail to exist? A. B. C. D. E. ( ) 1 lim x f x exists for all of the functions above. 3. The graph given shows that if 0 6 < - < δ x , then ( ) 2 1 - < f x . Find δ as shown in the figure given that 1 ε = . A. 8 B. 6 C. 4 D. 2 E. 1
4. Use the table below to estimate the limit (if it exists): ( ) 1 lim x f x where ( ) 3 1 1 ln 1 - = > x , x f x x, x . x 0.9 0.99 0.999 1.001 1.01 1.1 ( ) f x 0.27100 0.02970 0.00300 0.00100 0.00995 0.09531 A. 1 B. 3 10 C. 0 D. 1 4 E. does not exist 5. Given ( ) 2 2 - = - x f x x , why does the limit, ( ) 2 lim x f x , fail to exist? A. The function is not defined at 2 = x . B. The function increases without bound as x approaches 2 . C. The function is not continuous at 2 = x . D. The function approaches a different number from the right side of 2 than from the left. E. The function oscillates between two fixed values as x approaches 2 . 6. To analytically determine the limit of ( ) 5 3 4 + - = - x f x x as 4 x you must find a function ( ) g x that agrees with ( ) f x at all points except 4 = x . Find ( ) g x . A.

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This note was uploaded on 06/21/2011 for the course MTH 150 taught by Professor Marioborha during the Summer '11 term at Moraine Valley Community College.

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MTH 150 Final Exam Review - MTH 150 FINAL EXAM PREPARATION...

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