F(x,y,z) = 3x2 √ y cos(3z) = 3x2y12 cos(3z), is given by ∇f(x,y,z) = ∂f ∂x i ∂f ∂y j ∂f ∂z k = 3y12 ∂ ∂x (x 2)i3x ∂ ∂y (y12)j ∂ ∂z (cos(3z))k = 3y12 ×2x 2 −1i3x × 1 2 y1 2 j −3sin(3z)k = 6y12 xi 3 2 x2y−1 2 j −3sin(3z)k = 6x √ yi 3 2 x2 √ y j −3sin(3z)k Click on the green square to returnSee Maple for the plot 7 Problem 16 dy dx = x(x2 1) 4y3 y(0) = − 1 √ 2 First, we notice that y 6= 0 Now separate the variables and integrate y4 = 1 4 x4 1 2 x2 C This might be a good time to solve for C C = 1/4, so y4 = 1 4 x4 1 2 x2 1 4 The right side of the equation seems to be a nice form Try some algebra to simplify itPlotting graphics3d Share Improve this question Follow asked Nov 29 '15 at 533 user user
How Do You Graph X 2 Y 2 1 Socratic
