Q: Find the centroid of the solid bounded by x² = 4y and y = 5x - x² about the x-axis.
A: We will draw the region and rotate it about x-axis to create a solid of revolution . We will need…
Q: Integrate f(x, y, z) = x2 +y – z over the line segments from (0, 0, 0) to (1, 1, 0) and then to the…
A: According to the given information, it is required to integrate the function over the line segment.…
Q: find a parametrization of the curve. The line passing through (1, 0, 4) and (4, 1, 2)
A: Given: A line is passing through the points 1, 0, 4 and 4, 1, 2.
Q: Find the gradient of f(x,y,z) = (x² + y² + z²) Vf|(−2,2,− 1) = ₁ + Oj + k (Type integers or…
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A: For directional derivative let us first compute derivatives
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Q: Calculate line integral F-dr where F(x, y) = (7x + y, 5x + 2y) and C is a rectangle with vertices…
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Q: A _____ is the set of points (x, y) in a plane such that the difference in distances between (x, y)…
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A: Proceed as shown
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Q: Find the normal vector to the surface z = xe™Y at the point (2,0, 2).
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Q: Choose the gradient of the function f defined by f(x, y, z)= In[1 + (17xy + xz +9yz)²].…
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Q: Find the centroid of the triangular region cut from the first quadrant by the line x + y = 3.
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Q: Differentiate, and make sure to show all your work: y = exin(2z) %3D
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Q: The gradient vector of the function f(x, y, z) = ln(yz) + x² is: Select one: (2x, /, // ) (2x, -, -…
A: gradf =∇f =i∂∂x+j∂∂y+k∂∂zf .
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Q: Integrate f(x, y, z) = x2 -y + z over the line segments from (0, 0, 0) to (1, 1, 0) and then to the…
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Q: Find the maximum rate of change of f(x, y) = ln(x² + y²) at the point (3, 5) and the direction in…
A: Here is the solution of the given problem. Unit Direction:
Q: (2) The distance from the point (1, 2, -1) to the plane 3x - y + 2z = 6 is. (3) Consider the…
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Q: Find the equation of the normal line to the paraboloid z = 2x² +y² at the point (1,2,6). Select one:…
A: Equation of paraboloid To find: The equation of normal at a point P = (1,2,6).
Q: Let f(x, y, z) = x In y - exz.Calculate the directional derivative of fat point (-5, 1, -2) and…
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Q: Integrate f(x, y, z) = x2 +y – z over the line segments from (0, 0, 0) to (1, 0, 1) and then to the…
A: According to the given information, it is required to integrate the function over the line segment.…
Q: – 4V5 )ds]
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Q: Find the maximum rate of change of f(x, y) = ln(x² + y²) at the point (5, 2) and the direction in…
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Q: Does the the paraboloid z = 1 – 2x² - - y² have a tangent plane at some – x + y + z = 1?
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Q: Calculate line integral F-dr where F(x, y) = (7x + y, 5x + 2y) and C is a rectangle with vertices 0,…
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Q: Q1,- A- Locate the centroid (X only) of the shaded area y=12-3x Fig.L.A
A: X= My/M Y= Mx/M X,Y are coordinate of centroid.
Q: Find the centroid of the region bounded by these curves. y=2x+4, y=2x2
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Q: Find a point on the ellipsoid 3x2 + y2 + 3z2 = 1 where the tangent line is parallel to the plane…
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Q: Find the centroid when revolved in y-axis: y³ = x² ; y = 4.
A: As per the question we are given a solid of revolution obtained by rotating the area between y3 = x2…
Find the linearization L(x,y,z) of the f(x,y,z)= 8 square(x^3+y^3+z^3) at the point (1,2,3)
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Solved in 2 steps with 2 images
- Integrate f(x, y, z) = x2 -y + z over the line segments from (0, 0, 0) to (1, 1, 0) and then to the point (1, 1, 1).Integrate f(x, y, z) = x2 +y – z over the line segments from (0, 0, 0) to (1, 0, 1) and then to the point (1, 1, 1).what local linearizatoin of the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1) (show all steps please)
- Find a vector tangent to the curve of intersection of the two cyclinders x2+y2=32x2+y2=32 and y2+z2=32y2+z2=32 at the point (−4,−4,4)(−4,−4,4).. Find work done by the gradient of f(x, y, z) = zexy- 2y2/z along the path from (1, 2, 4) to (-1, 0, 5)Find a vector normal to the cylinder x2 + z2 = 8 at (2, 0, 2) by finding the gradient of the function f(x, y, z) = x2 + z2 at (2, 0, 2).