Homework Solutions - Section 16.5

Solutions to homework from section 16.5

#8 r_u = u³v²t² [ 4cos(ut²) - ut² sin(ut²) ]
r_v = 2u⁴vt² cos(ut²)
r_t = 2u⁴v²t [ cos(ut²) - ut² sin(ut²) ]

#12 dw/dt = (3t² - 2t - 2e^-2t) / (e^-2t + t³ - t²)

#16 dy/dx = (-4x³ - 4xy² + 3y³ - 2) / (4x²y - 9xy²)

#22 z_x = (-2xy + yz sin(xyz)) / (2z - xy sin(xyz))
z_y = (-x² + xz sin(xyz)) / (2z - xy sin(xyz))

#28 ≈ 0.076 in/min

Back to the page of homework assignments.

#8	r_u = u³v²t² [ 4cos(ut²) - ut² sin(ut²) ] r_v = 2u⁴vt² cos(ut²) r_t = 2u⁴v²t [ cos(ut²) - ut² sin(ut²) ]
#12	dw/dt = (3t² - 2t - 2e^-2t) / (e^-2t + t³ - t²)
#16	dy/dx = (-4x³ - 4xy² + 3y³ - 2) / (4x²y - 9xy²)
#22	z_x = (-2xy + yz sin(xyz)) / (2z - xy sin(xyz)) z_y = (-x² + xz sin(xyz)) / (2z - xy sin(xyz))
#28	≈ 0.076 in/min