Q18:- Find the magnitude of the maximum and minimum directional derivatives of the function w = x - 3xy – y³ + 2xz2 + 6yz, at the point Po(-1,2,2) and the unit vector of cach one.

Q: Represent the plane curve by a vector-valued function. x2 /16−y2/ 4= 1

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Q: Find a unit vector that is normal to the level curve of the function f(x, y) = 3x + 6y at the point…

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Q: Find a vector function that represents the curve of intersection of the paraboloid z = 7(x^2) +…

A: We have to find vector function that represents the curve of intersection of the paraboloid z =…

Q: Find a vector tangent to the curve of intersection of the surfaces given by x² + y² + z² = 1 and 2²…

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Q: 6. Find the unit vector for which the directional derivative Duf(x,y) of f(x,y) = %3D 3x2 + 4y2 at…

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Q: Find the directional derivative of f(x, y, z) = zy + xª at the point (2, 1, 3) in the direction of a…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Let F(x,y,z)=3x2+3y2+4z2. For which unit vector 0 will the directional derivative D0F at  (12,12,12)…

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Q: Find a vector which is tangent to the curve of intersection of the surfaces z = x² – y? and xyz + 30…

A: We will find out the required tangent vector.

Q: Represent the plane curve by a vector-valued function. x- + y2 = 4 r(t) = 2 cos ti +2 sin tj

A: x2 + y2 = 4 x2 + y2 = 22 = r2 Therefore, r = 2

Q: For the function f(x,y)=x^3−2x^2y−y^2−y, which vector is normal to the level curve at the point…

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Q: ü=i- where Use directional derivative definition to find Df (2.1) for the unit vector f(x y) = xy +1

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Q: Calculate the directional derivatives of the function x²y x²+ y? for (x, y) +0 f(x,y) = for (x, y)…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: B. Find the directional derivative of the function f(x.y): X-y at the point (1.-1) Duts xy+1 in the…

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Q: Find the directional derivative Duf(P) of f(x, y, z) = x²y?z²at the point P(1, 2, 3) in the…

A: We have to find the directional derivative of f(x,y,z).

Q: Ex.: Find the directional derivative of the function f(x, y) x'y + x'y at the point (1,1) in the…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: 4. Determine the directional derivatives of $(x, y) = tan"2+3 sin ). at the point (1,1) in the…

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Q: a)What is the slope of the tangent line to the curve y=2sin4x  at x=⊼(pie)/4? b) Find a unit vector…

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Q: Find the directional derivative of f(x,y) = x² + y² – 2x – 4y at the point (-2,3) in the direction…

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Q: (a) Find the directional derivative of the function f(x, y) = 4.xy – x2 – y? in the direction of…

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Q: Which of the following vector functions represents the curve of intersection of the cylinder x2 +y =…

A: Given Data: The equation of the curve is: x2+y2=4 ......1 The equation of the plane is: x+z=3…

Q: b. Find the directional derivative of the function z = x3 – y3 at the point M(1,1), in the direction…

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Q: Compute the directional derivative of f(r.y) = at the point (1, 1) in a direction normal to the…

A: Given that: f(x,y)=x2y at the point (1,1) Ellipse: x2+2y2=1 at the point (1,0)

Q: Find the directional derivative of the function f(x, y) = 2x2y + 6xy at (1, 1) in the direction of a…

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Q: b. Find the directional derivative of the function f(r, y, z) = re" + ye + ze" at the point (1, 1,…

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Q: #3. Consider the function xy2 if (x, y)# (0,0), f (x, y) = {x2+y2 if (x, y) = (0,0). Calculate the…

A: Given function is fx,y=xy2x2+y2if x,y≠0,00          if x,y=0,0 We have to calculate the directional…

Q: Represent the plane curve by a vector-valued function. x2 + y2 = 25

A: It is given that, x2 + y2 = 25. Let x=5cost and y=sint , Then 5cost2+5sint2=25cos2t+sin2t=25

Q: Compute the directional derivative of f (x,y)= at the point (1,1) in a direction normal to the…

A: The directinal derivative is given below

Q: a) What is the rate of change of f(x, y) = 3xy + y^2  at the point (2, 4) in the direction of vector…

A: (a) Given Data: Function: f(x, y)=3xy+y2 Point: (x, y)=(2, 4) Direction of vector: v=-3i-j The…

Q: B-For the surface z² = x² + y² find the directional derivative at the point (√2, √2,-2) in the…

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Q: Find the directional derivative of the function f = In (x² + y2) at the point P(4,5) in the…

A: By Bartleby policy I have to solve only first one as Q)3)a) and Q)3)b) are unrelated  problems.These…

Q: 7. Let f(x,y)=9-x² – y² a. Find the maximum value of the directional derivative at the point (1,2)…

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Q: Q19:- Find the magnitude of the maximum and minimum directional derivatives of the function w =…

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Q: Find a unit vector that is normal to the level curve of the function f(x, y) = 5x + 6y at the point…

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Q: Find the directional derivative of o = x2 + 2xyz – yz? at the point (1, 1, 2) in the direction of…

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Q: Find a vector that gives the direction of maximum rate of increase for the e2y cosx at (n/4,0).…

A: Consider a function . Then the maximum rate of change of this function occurs at the direction of…

Q: Q18:- Find the magnitude of the maximum and minimum directional derivatives of the function w = x3 –…

A: Directional derivative are given by gradient of function

Q: Choose the direction vector for which the function f defined by f(x, y)= sin(5x) cos(3y) has the…

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Q: Compute the directional derivative of the function f(x,y) = - xy + y at the point P(0, - 9) in the…

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Q: Q1. Find the directional derivative of = x²z + 2xy² + yz2 at (1, 2,-1) in the direction of vector…

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Q: a. Find the direction in which the directional derivative of f(x,y), at the point (z, y) = (0,4),…

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Q: The directional derivative of f(x, y, z) = x? + y? + 4xz at Po(1,-2,2) in the direction of the…

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Q: Let F(x, y, z) = 5x² + 2y2 + 522. For which unit vector 0 will the directional derivative DoF at (2,…

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Q: (iii) Find a vector equation for the tangent line to the curve of intersection of the cylinder a² +…

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Q: What is the directional derivative of f(x, y) = 4xy+ y cos x at the point (0, 1) in the direction of…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: Solution

Q: Calculate the directional derivatives of functions f(x, y)= x? – y? .2 in the direction of the…

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Q: Find the directional derivative of the function f(x, y) = In(at + y) at the point (- 1, - 2) in the…

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