5. x² +7y° For the function f(x,y)= x° find f, fy, f,(-5,-4), and f (0.-2). + y
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A: Here given function as fx, y=6-x2-y2 or z=6-x2-y2 .....1
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A: Equation of Normal
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A: The detailed solution is as follows below:
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Q: 04|| Find ôw/ôr and ôw/ôs as function of r and s, if: w = 2x + 3y² + 4z, X =r + s, y= cos (r - s), z…
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A: Please refer the attached image for complete solution.
Q: 6. If y is a differentiable function of r and 24 + 2y5³ 5y2, then find - dy da
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- A heat-seeking particle is located at the point (2, −3) on a metal plate whose temperature at (x, y) is T(x, y) = 20 − 4x2 − y2. Find the path of the particle as it continuously moves in the direction of maximum temperature increase.A heat-seeking particle is located at the point (2, −2) on a metal plate whose temperature at (x,y) is T(x, y) = 10 − x^2 − y^2. Find the path of the particle as it continuously moves in the direction of maximum temperature increase.Find the point on the ellipse x = 2 cos t, y = sin t, 0 <=t<= 2pai closest to the point (3/4, 0). (Hint: Minimize the square of the distance as a function of t.)
- Find the point on the ellipse x = 2 cos t, y = sin t, 0 ≤ t ≤ 2π, closest to the point (3/4, 0). (Hint: Minimize the square of the distance as a function of t.)A particle moves on a straight line with velocity function v(t) = sin ωt cos2ωt. Find its position function s= f (t) if f(0) =0A particle moves on a straight line with velocity function v(t) = sin(ωt) cos2(ωt). Find its position function s = f(t) if f(0) = 0.
- A car moves along a line at time, t, where it’s position is s(t) = 5sin(6t). Determine the velocity and acceleration at 10 sec and determine if it is speeding up or slowing down at 10 sec.A particle moves in a straight line with the velocity function v(t)=sin(wt) cos^5(wt). Find its position function x=f(t) if f(0)=0.Find the differential of f(x,y)=sqrt(x^2+y^2+36) at the point (2,3) df=------- Then use the differential to estimate f(1.94,3.02) f(1.94,3.02)=-------
- Find the exact length of the curve. y = 3 +1/2 Cosh 2x, 0≤ x ≤ 1The temperature in degrees Celsius on the surface of a metal plate is given by T(x, y), where x and y are measured in centimeters. Find the direction from point P where the temperature increases most rapidly and this rate of increase. T(x, y) = 80 − 3x2 − y2, P(−1, 5)A heat-seeking particle has the property that at any point (x, y) in the plane, it moves in the direction of maximum temperature increase. If the temperature at (x, y) is T(x, y) = -e-2y cos x, find an equation y = ƒ(x) for the path of a heat-seeking particle at the point (π/4, 0).