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 θ above the horizontal at which it is thrown. Use the accompanying table and the equations below to estimate the partial derivatives. fx(x0,y0)= limΔx→0f(x0+Δx,y0)-f(x0,y0)Δx; fy(x0,y0) =limΔy→0f(x0,y0+Δy)-f(x0,y0)Δy 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 v when v=80ft/s and θ=45∘.
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 θ above the horizontal at which it is thrown.
Use the accompanying table and the equations below to estimate the partial derivatives.
fx(x0,y0)= limΔx→0f(x0+Δx,y0)-f(x0,y0)Δx; fy(x0,y0) =limΔy→0f(x0,y0+Δy)-f(x0,y0)Δy
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 v when v=80ft/s and θ=45∘.
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