Calculus 1

Content Covered:

- Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces

- Quadric Surfaces

- Partial Derivatives

- The Chain Rule

- Maxima and Minima of Functions of Two Variables

Directions:Kindly answer each of the following problems below. And also, please indicate the complete solution. I promise that I will give you a good rating after this. Thank you so much for helping me out.

1) Note:The blue icon with i means "Exact Number, No Tolerance."

Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at which it is caught by Ryan. If we ignore air resistance, the horizontal range r of the baseball is a function of the initial speed v of the ball when it leaves Nolan's hand and the angle 0 above the horizontal at which it is thrown. SPEED v (ft/s) 75 80 85 90 35 165 188 212 238 40 173 197 222 249 ANGLE O (degrees) 45 176 200 226 253 50 173 197 222 249 Use the accompanying table and the equations below to estimate the partial derivatives. fx (xo, yo) = lim f (xo + Ax, yo) - f (xo, yo) . ;fy (xo, yo) = lim f(xo, yo + Ay) - f (xo, yo) 4x-0 4x Ay-0 Ay Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer. (a) Estimate the partial derivative of r with respect to u when u = 80ft/s and 0 = 40. or ~ i du(b) Estimate the partial derivative of / with respect to 0 when u = 80ft/s and 0 = 40. or i2 Find the points on the surface at yz = 4that are closest to the origin. Enter your answers in order of ascending x-coordinate. (x,y,z):( In (x,y,z)=( n n a n I J n