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20b_00f_fe - Math 20B(Bender Final Exam Fall 2000 •...

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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, I’ll 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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20b_00f_fe - Math 20B(Bender Final Exam Fall 2000 •...

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