QI/ Find the tangent plane of the function f(x,y) = 2x² + 2y2 at (1,1). Is it parallel to the plane x – 2y +z = 1 or not?

Q: Caleulate fe xydx + 3y'dy where C is the curve in xy plane, x = y from (0,0). to (1,3).

A: Solve the integral by substituting the curve in the question.

Q: Find the maximum rate of change of f(x, y, z) = x + y/z at the point (1, 1, -5) and the direction in…

A: We have to find the maximum rate of change

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: we have to find the directional derivative of f

Q: Please show your answers to at least 4 decimal places. Find the directional derivative of the…

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Q: Calculate directional derivatives and gradients in three dimensions. Find an equation for the…

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Q: a. Find the directional derivative of the function u = xyz at the point M(1,1,1), in the direction…

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Q: 4. Determine the directional derivative of f(r, y, z) = xe"+rsinz+a²y at the point (2,0, ) in the…

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Q: Solve for an equation of tangent plane and parametric and symmetric equations of normal line to the…

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Q: A surface S is described by the equation f(x, y, z) = n where f(x, y, z) = yz + nx²y+ yz³ (a) Find…

A: Given fx,y,z=yz+nx2y+yz3 Substitute n=5 Hence, fx,y,z=yz+5x2y+yz3 (a) We have to find the equation…

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z2 (5,…

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Q: Find the moment of inertia: y = x - x²; y = 0 about y = 0.

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Q: Find the moment of inertia: x = y +1; y = 1; y = 2; x = 0 about x-axis.

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Q: Find the directional derivative of the function f(x, y, z) = ryz in the direction normal to the…

A: We havefx,y,z=xyz

Q: Determine the directional derivative of f(x,y, z) = tan where u = (-1,2,2) at P(0,1, 1). Determine…

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Q: Find the maximum rate of change of f(x, y, z) = x + y/z at the point (-3, -1, 3) and the direction…

A: As per honor code, we are entitled to solve only one question at a time so I am providing the same.…

Q: Tangent to the parabola z = x² + 3y² , x = 1 , at point ( 1, 2, 13

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the maximum rate of change of f(x,y, z) = r + y/z at the point (-1, -3, 5) and the direction in…

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Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 − 4z2 = 21,    (−3,…

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Q: Find the directional derivative of the function f(x,y, z) = V22+ y² + z² at point (2, -3, 6) in the…

A: In this question, we want to find the directional derivative of the given function at given point…

Q: Find the Directional derivative of the function f(x,y,z) = /x² + y² + z² from point (1,2, –2) in the…

A: The objective is to compute the directional derivative of the function fx,y,z=x2+y2+z2 from point…

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² y2 + z2 (3, 5,…

A: To find the gradient of the function at the point given

Q: Find the tangent plane to the equation z = 3x? – – 60) - y² – 4y at the point (4, 2, - -

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Given that  The f(x,y)=4y√x  P(4,3) To find teh maximum rate of change and direction vector

Q: Find the tangent plane to surface 8x2 + y2 + 4z2 = 25  at the point ( 1, -1, 2 )

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z2 (2,…

A: We have to find maximum value of the directional derivative at the given point.

Q: Example: find the tangent plane and normal line of the surface f(x, y, z) = x + y' +z-9=0 at the…

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Q: 5. Are there any points on the graph of x2 - y? – 22 = 1 where the tangent plane is parallel to the…

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Q: Find the maximum rate of change of f(x, y) Maximum rate of change: = In(x² + y?) at the point (3, 1)…

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Q: A particle moves in the xy− plane according to the law x=at, y=bt2, where a>0, b>0. Determine…

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Q: The two surfaces x2 + y2 + z2 = 6 and 2x² + 3y2 + z2 = 9 intersect at the point(1,1,2). Find the…

A: Given: The two surfaces  x 2 + y 2 + z 2 = 6  and  2 x 2 + 3 y 2 +  z 2 = 9. The given two surfaces…

Q: Example: find the tangent plane and normal line of the surface f(x, y, z) = x + y° +z-9=0 at the…

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Q: Find the directional derivative of the function at pointP in the direction of v. f(x, y, z) = y² +…

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Q: (a) What is the maximum directional derivative of g(x, y) = y²e2¤ at (2, – 1) and in the direction…

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Q: Equahon of tangent plane to surface of function at (כו,נ ,C Fex,y)=2x?+Zy*+* *2y-2

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z² (7,…

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Q: Sketch the trace of f in the xz-plane. Find the directional derivative of f in the direction of the…

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Q: Find the maximum rate of change of f(x, y) = In(x² + y²) at the point (1, -4) and the direction in…

A: Here, the given function is: f(x,y)=ln(x2+y2)

Q: A surface S is described by the equation f(x, y, z) = n where f(x, y, z) = yz + nx²y+ yz³ 3 (a) Find…

A: Given f(x, y, z) = yz + nx2y + yz3 ∇fP⋅P=0 Now,…

Q: (b)Find the directional derivative of f(x,y,z) = x²y- yz3 + z %3D at point (1,-2,0) in the direction…

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Q: Find the directional derivative of the function: f(x, y) = ez² + 4y at the point (0, 0) in the…

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Q: Find the gradient of the function at the given point. Function Point F(x, y, z) = Vx2 + y² +. (5, 4,…

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Q: 9. Find equations of tangent plane and normal line of surface e -z+ xy 3at point(2,1,0). %3D

A: Given a surface fx,y,z=ez-z+xy=3. To determine the equation of the tangent plane of the surface at…

Q: Compute the directional derivative of f(x, y, z) = y²e*y% at the point (0, 1, -1) in the direction…

A: We will find out the required value.

Q: Please show your answer to 4 decimal places. Find the direction in which the maximum rate of change…

A: We have to find the direction in which the maximum rate of change occurs for function…

Q: the max and min directional derivative and their directions; (4) the parametric equation of the…

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Q: Find an equation for the tangent plane to the surface z + 4 = ry* cos(z) at the point (4, 1, 0)

A: Solution: The objective is to find an equation for the tangent plane to the given surface

Q: Find the maximum rate of change of f(x, y) = In(x² + y²) at the point (3, 5) and the direction in…

A: This is a problem related to the derivative of the function. For calculating the maximum rate of…

Q: Solve for an equation of tangent plane and parametric and equations of normal line to the given…

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² + y² + z² (5,…

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Q: Find the gradient of f(x, y, z) = xy tan (3z) at the point (x, y, z) - 3, 2 Find exact values. No…

A: Given,