Math 19B Migliore Exam - THESE QUESTIONS ARE FROM AN ACTUAL...

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THESE QUESTIONS ARE FROM AN ACTUAL OLD EXAM. YOUR EXAM WILL RESEMBLE THIS EXAMPLE OF AN OLD EXAM IN DEGREE OF DIFFICULTY AND LENGTH. THE ACTUAL QUESTIONS MAY OR MAY NOT BE SIMILAR. FOR A LIST OF TOPICS THAT YOU ARE RESPONSIBLE FOR PLEASE SEE Review for Exam 1 ” ON THE SYLLABUS WEBPAGE. 1. Express the definite integral as the limit of a Riemann sum. Explicitly define all expressions you use. 5 sin(x)dx 2. Approximate the definite integral 2 x 3 dx x as a sum. Use four equal subintervals and right endpoints. 3. Find the derivative dy dx if 5 x y ln(t )dt = . Be sure to show your work and give the statement of any theorems that you use. 4. Given the graph of y f (x) : a) Find 3 f (x)dx . b) Find the average value of f on [ ] 3,8 . 5. Find the general antiderivatives for the following functions: a) 2 x 3x 1 f (x) x + = b) 2 g( ) sec θ = c) ( ) lnx h(x) x = 0 1 2 3 4 5 0 1 2 3 4 5 6 7 8 9 2 4 3 = 8 3
Math 19B - Exam #1 Page 2 Fall 2002 - Migliore 6. Use the Fundamental Theorem of Calculus to evaluate the following definite integrals. a) 1 1 x dx x + b) 2 1 0 xe dx 7. Find N(t) if 5t dN 3e dt = and N(0) 4 x
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