limit definition of a derivative

1. (4) Use the limit definition of a derivative to show that 2. (8) Use the limit definition of a definite integral to find . . 3. (4) Find the extreme values of . Then, find the equation of the line tangent to y at its point of inflection. Label your answers clearly. Answers must be exact (no decimals). 4. (4) Find these limits. 5. (4) 6. (4) Last year in a baseball game, Christian Vázquez hit a line drive and started running towards 1st base at a constant 7.2 m/s. Xander Bogaerts was on second base. He started with a 2m lead off and ran with a constant speed of 8 m/s towards third base. How quickly is the distance between the two runners changing when Bogaerts reached third? All of the bases are corners of a square with 27.4 m sides. 7. (7) Calculate using the Fundamental Theorem of Calculus. 8. (8) Approximate using 5 middle rectangles. (Be sure to show all calculations!) 9. (10) The Chili Peppers are coming to ACL on October 14th!! People will come into their concert area at a rate of people per hour for the first 2 hours the gates are open. No one is in the concert area before t=0. At t=2, the entrances will be closed off and the concert will begin. (A) How many people make it to the show? (B) At what rate is the crowd changing when t=2? (C) Find the time at which the rate of people entering is a maximum. Justify your answers. 10. (7) Find . 11. (8) The graph is of . Let . Find: 12. Find the derivatives/antiderivatives/integrals, if possible. Label each problem if doing on your own paper. (4pts each) a) b) Find specific solution where F(x) is the antiderivative of c) . d) e) f) g) h)
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