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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 of the baseball is a function of the initial speed of the ball when it leaves Nolan's hand and the angle 8 above the horizontal at which it is thrown. SPEED U (ft/s) ANGLE (degrees) Use the accompanying table and the equations below to estimate the partial derivatives. f(xo + 4x₂ yo) — ƒ(x0, 30) f(xo» 30 + 4y) — f(xos 30) Ay Ax f(xo yo) = lim xx40 75 35 165 40 173 45 176 50 173 22 ar 28 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 with respect to v when v = 80ft/s and 8 80 85 90 188 212 238 197 222 249 200 226 253 197 222 249 22 (b) Estimate the partial derivative of with respect to 8 when v = fy(xoyo) = lim 4y→0 i 80ft/s and 8 = 45°. = 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 of the baseball is a function of the initial speed of the ball when it leaves Nolan's hand and the angle 8 above the horizontal at which it is thrown. SPEED U (ft/s) ANGLE (degrees) Use the accompanying table and the equations below to estimate the partial derivatives. f(xo + 4x₂ yo) — ƒ(x0, 30) f(xo» 30 + 4y) — f(xos 30) Ay Ax f(xo yo) = lim xx40 75 35 165 40 173 45 176 50 173 22 ar 28 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 with respect to v when v = 80ft/s and 8 80 85 90 188 212 238 197 222 249 200 226 253 197 222 249 22 (b) Estimate the partial derivative of with respect to 8 when v = fy(xoyo) = lim 4y→0 i 80ft/s and 8 = 45°. = 45°.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 67E
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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 of the baseball is a function of the initial speed v of the ball when it leaves Nolan's hand and the angle & above the horizontal at which it is thrown. SPEED U (ft/s) 75 80 85 35 165 188 212 8 5 ANGLE 0 (degrees) 40 173 197 222 249 200 226 253 197 222 249 45 176 85 | 22 50 173 Use the accompanying table and the equations below to estimate the partial derivatives. - ¸„ƒ(xo + Ax‚ yo) − f (xos 30) f(xo» 30 + 4y) − f(xo, 30) Ay Ax f(xo, yo) = lim 4x→0 28 22 90 238 -ify(x0, 30) Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer. i = (a) Estimate the partial derivative of with respect to v when v = 80ft/s and 8 = 45°. lim 4y→0 (b) Estimate the partial derivative of x with respect to 8 when v = 80ft/s and 8 = 45°.
Transcribed Image Text: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 of the baseball is a function of the initial speed v of the ball when it leaves Nolan's hand and the angle & above the horizontal at which it is thrown. SPEED U (ft/s) 75 80 85 35 165 188 212 8 5 ANGLE 0 (degrees) 40 173 197 222 249 200 226 253 197 222 249 45 176 85 | 22 50 173 Use the accompanying table and the equations below to estimate the partial derivatives. - ¸„ƒ(xo + Ax‚ yo) − f (xos 30) f(xo» 30 + 4y) − f(xo, 30) Ay Ax f(xo, yo) = lim 4x→0 28 22 90 238 -ify(x0, 30) Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer. i = (a) Estimate the partial derivative of with respect to v when v = 80ft/s and 8 = 45°. lim 4y→0 (b) Estimate the partial derivative of x with respect to 8 when v = 80ft/s and 8 = 45°.
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