Q11// Evaluate f, grad V dS where V = x + y? + z² and S is the surface x2 + y2 = 4 bounded by z=0,z=4 ,x30,y%3D0? %3D

Q: Evaluate ʃC F dr where C is the parabola y = x2 from (0, 0) to (2, 4) and F (x, y) =< −ysinx,…

A: Given a curve C is a parabola from (0, 0) to (2, 4)

Q: For a given surface z-x^2-y^2=10 Find the parametric representation of the straight line which…

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Q: Sketch the surface 1≤z≤ √9-x² - y² 1≤z≤√9-x² - y² and_x² + y² ≤1

A: Given is the surface surface 1≤z≤9-x2-y2 and x2+y2≤1 The objective is to sketch this surface.…

Q: Find normal line (parametric form) to the surface x^2 − 4y^2 + z^2 + y = 27 at the point (5, 1, −3

A: This question is about application of derivative

Q: n exact form. Use symbolic notation and fractions where needed.)

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Q: Find the equation of the tangent plane to x2 the surface z = 4 + y? at the point (2, –2, 5)

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Q: the normal line of the surface [z = (4x^2 + y^2] at the point (1,1,5) O 8x-2y+z=5 O 8x+2y+z=5…

A: We have to find the normal line of the surface.

Q: Suppose that the plane tangent to the surface z = f(x, y) at (-4, 2, 5) has equation z + 5x + 4y =…

A: From the equation of tangent, we can derive: z = -(7 + 5x + 4y) Hence,

Q: Describe and sketch the surface given by the function.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: / Find the distance from the line x 2 + 1, y 1 +1, z = -(1/2) - (1/2)t to the plane x + 2y + 6z 10.

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Q: Sketch the surface 1≤z≤√√9-x²-y²_and_x² + y² ≤

A: Solution is below

Q: What is the equation for the tangent plane to the surface z = 4x°y2 + 2y - 2 at the point P(1, -2,…

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Q: use the lagrange multiplier to find extreme points of f(x,y,z) = 2x+z over the intersection of…

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Q: Draw a contour map for f(x,y) = x^2 + 4y^2 where k = 3, k=8 and k=14

A: A scalar function f(x,y) is a rule that is used to associate a number, or quantity with a particular…

Q: What kind of surfaces are the level surfaces f(x, y, z) = const? f = 4x - 3y + 2z

A: As per the question we are given a trivatiate function : f(x, y, z) = 4x - 3y + 2z And we have to…

Q: Find the extreme values of the function f(x, y, z) = xy + z^2 on the circle in which the plane y - x…

A: Given function is fx,y,z=xy+z2. We have to find the extreme values of the given function on the…

Q: Q1.6 Find the point on the surface given by the equation x^2 + 5y^2 + 10z^2 = 18016 that has a…

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Q: Q3: Find the points on the surface x^2+z^2-6=0, closest to the origin.

A: Given: x2+z2-6=0 Let x,y,z be the point on surface x2+z2-6=0 which is closet to point 0,0,0 Then the…

Q: Which surface below is an elliptic paraboloid? O x^2 + y^2/4 - z^2 = 1 O z = -sqrt(x^2 + y^2) z =…

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Q: Sketch the surface 1<z</9-x² - y² and x²+y² <1

A: To sketch the given surfaces.