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Unformatted text preview: Math 20B (Bender) Final Exam Fall 2000 Please put your name, ID number, and section number (or time) on your blue book. The exam is CLOSED BOOK, but you may use a page of notes. Calculators are NOT allowed. You must show your work to receive credit. If you email me your name, section and ID number, Ill reply with your grade. 1. (20 pts.) Evaluate the following. Remember to show your work! (a) lim x e x- 1 sin x (b) (1 + i ) 30 where i = - 1 2. (60 pts.) Evaluate the following. Remember to show your work! (a) Z 2 x 3- x dx (b) Z e 1 ln x dx (c) Z sin 4 x cos 3 x dx (d) Z 1 t t 2- 1 dt 3. (15 pts.) Find the three cube roots of 1 + i . You may leave sines and cosines in your answer, but not inverse trig functions. 4. (20 pts.) The region bounded by y 2 = 4 x + 4, x = 8, the x-axis and the y-axis is rotated about the x-axis. Write down integrals for the volume and surface area....
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