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# FinalReview3 - r7l I sins r dr JO using the Simpson's rule...

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Math 1710 Final Review 7 33. A woman is in a boat 100 meters from shore. If she can row the boat at the rate of 1 meter per second and she can walk on shore at the rate of 2 meters per second, find her fastest path to a point 200 meters down the (straight) shore. 3 Prove that if f'(r) : g'(r) for every real number r, then there is a constant c such that /(r) : g(r) * c for every real num- ber r. Find the area bounded by the functions f(r): sinr and g(r): r(r - n). Find the area bounded between the graphs of. r-y2 +I: 0 and r-a - 1 : 0. Find the volume of a room whose floor is an ellipse with equation ! + + :1 and whose cross section is a semicircle when sliced perpendicular to the z-axis. Find the value of n needed to estimate l1f I sin3 r dr Jo using the trapezoid rule if you want your estimate to be within 0.0001 of the cor-
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Unformatted text preview: r7l I sins r dr JO using the Simpson's rule if you want your estimate to be within 0.0001 of the cor-rect answer. Use the n you found to es-timate the integral. Derive the formula for the volume of a cone with base radius r and height h. Find the volume generated if the region in the piane between r : 0 and tr : T, below y : \/sitr, and above the r-axis is rotated about the r-axis. 46 47. 49. 50. 34. 35. 36. J/. 38. 52. (2 40. 4L. i.) +2. 43. 44. r Compute J sin2r dr in two ways. r1 !_ra, Compute J -cos- , compute 14 2r2 + 3r - r o* 'Jt{r , I sin2 2r comPute J "."rrr"d' r4 Compute Jo rt/12 * I dr 39. Comnute / dr Comoute ["""'r cofed"e J Use a limits of Riemann sums to com-r+ pute / (r' + I) dr. JI Compute limrr-- ZT:'W Compute lim",** Di:, sin(f;)fi. Prove the Mean Value Theorem using Rolles'Theorem. different 48. da. 45. Prove Rolles' Theorem....
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## This note was uploaded on 10/22/2010 for the course MATH MATH 1710 taught by Professor Brand during the Fall '07 term at North Texas.

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