MATH 41 Final: Stanford MATH 41 finalsol

• School: Stanford University
• Department: MATH - Mathematics
• Course: MATH 41
• Professor: All

Document Summary

1 + (e x)2 ( e x) 5 csc4(3x) ( csc(3x) cot(3x)) 3 + 1 + e 2x + 15 csc5(3x) cot(3x) + 2 x ln 2 (b) find dy dx in terms of x and y if: y + xy = 6 (5 points) we use implicit di erentiation: dy dx. 2 xy (cid:18)y + x dy dx(cid:19) = 0 = dy dx(cid:18)1 + dy dx x. Page 2 of 14: (9 points) a tall, open pot has the shape of a cylinder, with a circular base of radius 4 in. A marble with radius r inches, where 0 < r < 4, is placed in the pot, and the pot is lled with just enough water to cover the marble completely. We wish to compute the volume of water vw as a function of the radius r of the marble.