Find a unit vector in the direction in which ƒ(x,y) = √x² + y² increases most rapidly at P(π/6,π/4); and find the rate of change of ƒ at P in that direction.

Q: Find the orthogonal trajectories for the family of curves, sin? y C In x.

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Q: the Curve y=2x=3== r x + 20 where the tangent is parallel to the X-aXis Find the points on 12 X + 20

A: When the tangent is parallel to the x-axis, dy/dx will be equal to 0

Q: Verify that ƒxy = ƒyx, for ƒ(x, y) = xey.

A: Given function is fx,y=xey We have to verify fxy=fyx Solution: fxy means that first we find partial…

Q: Find the equation of the tangent plane to f(x, y) = x² - 2xy + 5y2 having slope 2 in the positive x…

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Q: Find the point at which the tangent to the curve y = v V4x2 +1– 2 | has its slop 2

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Q: Please review the screenshot attached to this request and solve the problem :)

A: Step 1:​(1) f(x,y)=2x2−x4+3y2at(2,3)Using the Power…

Q: XVII. For w = x³ + xy² +yz, find the rate of change of w at point (1,2,3) in the direction towards…

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Q: Round each component to four decimal places, if necessary. Find the gradient of f(x, y) = 4e³x/y +…

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Q: Find all points at which the direction of fastest change of the function f(x, y) = x² + y - 4x - By…

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Q: ind all the tangents to the curve y cos (x %3D

A: Here we have to find the tangents on the curve y=cos(x+y)...........(1)     , -2π≤x≤2π parallel to…

Q: Find the gradient of the curve y = x° – x2 – 8x – 2 at the point on - - - the curve whose…

A: As we know that; The expression for the gradient or slope; m=dydx And The Power law; ddxxn=nxn-1