MATH 100 Midterm: MATH100 Midterm 2 Practice

Evaluate each of the following line integrals. (a) c(t) = (2 cost), 2 sin(t)), x dy-y dx, JC 2π t (b) x dy + y dx, c(t) = (cos(t), sin(mt)), 2 t 4 (c)yz dx + xz dy + xy dz, where c consists of straight-line segments joining (1, 0, 0) to (0, 1, 0) to (0, 0, 1) (d) x2 dx-xy dy + dz, where c is the parabola z = x2, y = 0 from (-1, 0, 1) to (1, 0, 1)

3/4 points Previous Answers Mars VectorCalc6 7.2.004 Evaluate each of the following line integrals. (a) x dy-y dx, c(t)-(2 cos(t), sin(t)), 4π st 6m 4π (b) xdy + y dx, c(t) -(cos(7mt), 2 sin(mt)). 4 Sts6 (c) yz dx + xz dy + xy dz, where c consists of straight-line segments joining (3, 0, 0) to (0, 3, 0) to (0, 0, 3) (d) 2x2 dx-xy dy + dz, where c is the parabola z = 4x2, y = 0 from (-1, 0, 4) to (1, 0, 4) Submit Answer Save Progress Practice Another Version

Suppose z = x2 sin y, x = -5s2 + 2t2, y = -10st. Use the chain rule to find and as functions of x, y, s and t. = -20xssiny - 10tx^2cosy = 8xtsiny-10sx^2cosy Find the numerical values of and when (s, t) = (3, 4). (3, 4) = 2704.50 (3, 4) = 2895.27 Suppose w = x/y + y/z, where x = et, y = 2 + sin (2t), and z = 2 + cos (5t). Use the chain rule to find dw/dt as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite et as x. dw/dt = exp(t)/y + 2cos(2t)/z - 2xcos(2t) + 5ysin(5t)/z^2 Note: You may want to use exp() for the exponential function. Your answer should be an expression in x, y, z, and t; e.g. "3x - 4y" Use part A to evaluate dw/dt when t = 0. 1/y - 2/z - 2x/y^2