Find an equation of the plane that passes through the points (2, 4, 1), (2,2,-4), and (−3, 5, 3).

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A: The solution is shown in step-2

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A: we have given equation

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A: To find a formula for and to determine the slope  for the following function.

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A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 6) Find the interval of convergence of the power series. a) Σ k=0 Σ b) Σ n=1 (x-1)* k Χ n

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A: The given curve is And we have to evaluate the the integrals A) ,        B) ,      C)

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A: In this question , we will find the value.

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A: The given integral is:

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Q: 3 LET f(x) = (x - 1)² ESTIMATE THE AREA UNDER THE CURVE FRom X=0 TO X = 3 USING 6 RECTANGLES AND…

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Q: Solve the given equation. (Enter your answers as a comma-separated list. L 2 cos(8) 8 = = - 0 = 2…

A: Cos θ = -  √2/2

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A: A manufacturer of handcrafted wine racks has determined that the cost to produce  units per month is…

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Q: Calculate the partial derivative d using implicit differentiation of x'w+w8 + wz² + 7yz = 0. dz (Use…

A: Given :Calculate the partial derivative using implicit differentiation.

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Q: Find the line integral of f(x,y,z) = x+y+z over the straight-line segment from (3,2,4) to (2,1,2)…

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Q: If four forces are acting on an object then the sum of the forces is called the resultant force.…

A: The resultant force, also known as the net force, is the single force that represents the combined…

Q: = (7y² - 3x²)i + (3x² + 7y²) j and curve C: the Use Green's Theorem to find the counterclockwise…

A: C: The triangle bounded by , and .

Q: = S F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = yzi + 7xzj+exyk, C…

A: Given:Since we have given the and circle is  To Evaluate: where C is oriented counterwise.

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A: we have given series

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Q: Use the transformation u=x+4y, v=y-x to evaluate the given integral by first writing it as an…

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Q: e2x-1 10 Cost 1 (4) Find the limit: lim

A: The given limit is,

Q: 10.5 3.5 10.5 Let + [10 f(x) dx = 9, [." *F(x) dx = 2, and [... (a) [F(x f(x) dx = 4 7 (6f(x) — 5)…

A: Concept

Q: Calculate the exact value of log, (5√25). 7 (B) (C) (D) - 5 5 (A) (B) 7 5 (E) 3

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Q: 340 The marginal profit function for a company is given by P'(x) = √x 2. Estimate the change in…

A: The marginal profit function for a company is given by

Q: 14 If √¹4 f(x) dx = -67 and F(14) = −62, where F(x) is an antiderivative of f(x), find F(3).

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Q: Sim (x-ex) X700

A: To evaluate the following limit.

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Q: Find the indicated derivative or integral: d da Answer: a. ·(3²x+1)

A: according to bartleby guide line we do only first part of multiple questions. please re post other…

Q: Use the divergence theorem to evaluate JS (3x + 5y + z²) ds where S is the sphere x² + y² + z² = 1.

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Q: Find the centroid (x, y) of the region bounded by 2x² + 5x, y = 0, x = 0, and x = 1. : Y Y =

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: a(x,y) Find the Jacobian a(u,v) x = u sin (3v), y = u cos (3v). for the transformations x = u cos…

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Q: Find the extreme values of f(x, y) = x^2 + 2y^2 − 2x + 3 subject to the constraint x^2 + y^2 = 10.

A: f(x, y) = x2 + 2y2 − 2x + 3 Subject to the constraint : x2 + y2 = 10Find the extreme values of f(x,…

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Q: Let f(x, y) = xy²and r(t) = (1,²,³). Calculate Vf. (Use symbolic notation and fractions where…

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Q: Given the equation x-6x³-5x²2 +24x+4=0, complete the following. a. List all possible rational roots.…

A: The solution is shown in step-2