Find an equation of the tangent plane to the surface at the given point. f(x, y) = Y, (1, 5, 5) %3D 10 10 X

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A: Given

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Q: Express the iterated integral as an equivalent integral with the order of integration reversed.…

A: Express the iterated integral as an equivalent integral with the order of integration reversed.

Q: an

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A: From the Maclaurin series expansion of sin x and cos x: sin x≈x-x33!+x55!-x77!+x99!-x1111!cos…

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Q: 16. Find the volume of the region that lies under the graph of the paraboloid z = over the rectangle…

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Q: If the length of arc of a circle of radius 2/3 feet is 14 feet. then the central angle 0 is:

A: Given Radius of circle (r)=23feet & Length of arc (s)=14 feet To find central angle θ:

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A:

Q: For each of the following series determine if the series converges or diverges. In(n) Σ n=2

A: Since you have asked multiple questions in a single request we would be answering only the first…

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A: answer is in next step

Q: Find V x (V × F) if F(x, y, z) = 4xyj+ 9xyz k. V x (V × F)

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Q: a) Consider the scalar function: f(x, y) = -4x*y³ – 2a*y? Find the gradient: Vf(x, y) = i+ Find the…

A: Given; f(x,y)=-4x^2y^3-2x^4y^2

Q: Consider the functions. f(u) = u³ + u g(x) = cos (x) Find the following function and derivatives.…

A: The given functions,fu=u8+ug(x)=cos(x)

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Q: Evaluate the integral / (2x + 6y)dx + (15x – y)dy a C arc y = x² from (0,0) to (1, 1). NOTE: Enter…

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Q: Find the area of the region enclosed by x2 and y = 5x by integrating with respect to y. the curves Y…

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Q: Consider the function f(x): - 4x + 6x - 8. f(x) has a critical point at x A. Find the value of A: A…

A: For critical points ofa function we first find the derivative of the function and equate it to zero.

Q: 7. -4 3. ) dx - 3 10.

A: The given integral,         ∫e5xe2x7+3e3xdx

Q: 2. Find the area of the parallelogram whose vertices are given by: P: (1,2, –1), P2 = (4, 2, -3), P3…

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Q: Find curl (9z i + 10x j+ 7y k). curl (9z i+ 10x j + 7y k) = ( i Di + ( i Oj + ( i )k

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Q: ind lim f(x) for the given piecewise function. x-4 2х + 5 if x 4 E the limit does not exist, enter…

A: Topic  = Limits

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A:

Q: What is the measure of the apothem of the hexagonal base? (c) What is the area of the hexagonal…

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Q: Edit Evaluate the line integral -ydx + xdy along the curve C : y = 21x from (21, 21) to (0,0). NOTE:…

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Q: Express the iterated integral as an equivalent integral with the order of integration reversed. r36…

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Q: dy Solve the derivative dx for the function: x = e'sint ; y = etcost

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Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

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Q: Use a double integral to find the volume under the plane z = 32x + y and over the rectangle R = {(x,…

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Q: Find the volume of the region enclosed by z = 1 – y? and z = y² – 1 for 0 < x < 21. V =

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Q: A particle is moving with the given data. Find the position of the particle. a(t) = t - 8, s(0) = 4,…

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Q: Evaluate the iterated integral. /8 3/y sin y dz dx dy Jo

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Q: Evaluate the definite integral. 9ti +3t'j + Vtk) dt

A: The given integral,          ∫-119t i+3t3 j+t3kdt

Q: Find the principal unit normal vectóř tô thể curve at the r(t) = /2ti + e'j + e-k, t = 0 %3D

A: Principal unit normal vector

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A:

Q: Find the curvature and the radius of curvature at the point t = 0. %3D = e' cos(t), y = e' sin(t), z…

A: Given

Q: A spring has a natural length of 22in. A force of 16001b stretches the spring to 32 in. How far…

A: We will use rules of spring stretch to solve it.

Q: 12. Find an equation for the tangent plane to the surface given by 2xy? = 2z2 – ryz at the point (2,…

A: We know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Where n→-nxi+nyj+nzk is…

Q: 8. The ideal gas law PV volume, and temperature of a confined gas, where n is the number of moles of…

A: We need to prove the statement.

Q: Skatch the curve in polar coordinates. r=I+ 3sino 2 -6 -4 -4

A: Given curve r= 1+ 3sin( theta)