MATH 2630 Final Exam Practice Problems

# In spherical coordinates the surface 2 1 cos2 16 is a

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Unformatted text preview: 33 5 √ 33 1 √ 32 2 √ 33 4 √ 32 MA 261 FINAL EXAM Fall 2001 Name: Page 3/11 3. In spherical coordinates, the surface ρ2 (1 − cos2 φ) = 16 is a A. half cone B. plane C. sphere D. cylinder E. saddle surface 4. The length of the curve ￿ (t) = (1 − 2t2 )￿ + 4t￿ + (3 + 2t2 )￿ 0 ≤ t ≤ 2 r i j k, is given by which integral A. ￿2 0 B. ￿ 16 t2 + 2 dt ￿2 ￿ 8t4 + 4t2 dt 0 C. ￿2 √ ￿2 4t dt ￿2 ￿ 4 2t2 + 1 dt 8t + 4 dt 0 D. 0 E. 0 MA 261 FINAL EXAM Fall 2001 Name: Page 4/11 5. Find the position vector ￿(1) of a particle with acceleration vector ￿ (t) = −10￿ , initial r a k velocity ￿ (0) = ￿ + ￿ and initial position ￿(0) = ￿ + 2￿ . v ij r i j A. ￿ + 2￿ i j B. 2￿ + 3￿ − 5￿ i j k C. ￿ + ￿ ij D. 2￿ − ￿ ij E. ￿ + ￿ − 5￿ ij k 6. The maximum value of 3x2 + 2y 2 − 4y given that x2 + y 2 = 16 is A. 40 B. 46 C. 60 D. 52 E. 64 MA 261 FINAL EXAM Fall 2001 7. The smallest value of x2 + y 2 + Name: Page 5/11 8 is x2 y 2...
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## This note was uploaded on 10/09/2013 for the course MATH 2630 taught by Professor Staff during the Fall '08 term at Auburn University.

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