M1550-Final-SG

M1550-Final-SG - Math 1550(30 Final Exam Study Guide The...

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Math 1550 (30) Final Exam Study Guide The Final Exam (worth 20% of your grade) will be on Thursday, December 9th, from 5:30 - 7:30PM. These problems should be a guide to prepare for the test. Sections you should focus on: Chapter 2: Sections 2.1 through 2.6 Chapter 3: Sections 3.1 through 3.7, and 3.10 Chapter 4: Sections 4.2, 4.3, 4.4, 4.7, 4.9 Chapter 5: Sections 5.2, 5.3, 5.4, 5.6, 5.7 Chapter 6: Sections 6.1, 6.2 (just average value), 6.3, 6.4 Chapter 8: Section 8.1. 1

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Chapter 2 Problems 1. For what value of c is the function below continuous on ( -∞ , )? f ( x ) = cx + 4 , if x < 2 cx 2 - 1 , if x 2 2. Find the limits: (a) lim x 4 x 2 - 16 x - 4 (b) lim x 4 x - 2 3( x - 4) (c) lim x 0 sin(8 x ) x (d) lim x 0+ sin(5 x ) | x | (e) lim x 0 - sin(3 x ) | x | (f) lim x 3 x - 3 x 3 - 9 x (g) lim x 0 5 + x - 5 - x x (h) lim x 0 tan(4 x ) tan(8 x ) ; 3. Below is the graph of a function f : 1 2 3 4 5 6 2 4 6 8 10 2
Find: (a) lim x 1 - f ( x ) (b) lim x 1+ f ( x ) (c) lim x 2 - f ( x ) (d) lim x 2+ f ( x ) (e) lim x 4 - f ( x ) (f) lim x 4+ f ( x ) State the type of dicontinuity that f has at the points x = 1, x = 2, and x = 4. 3

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Chapter 3 Problems 1. Find all the values of x where the tangent lines to y = x 3 3 + 3 x and y = 2 x 2 are parallel. 2. Determine the coefficients a and b such that p ( x ) = x 2 + ax + b satisfies p (1) = 4 and p 0 (0) = 1.
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