Proof of Stokes’ Theorem Confirm the following step in theproof of Stokes’ Theorem. If z = s(x, y) and ƒ, g, and h are functionsof x, y, and z, with M = ƒ + hzx and N = g + hzy, then           My = ƒy + ƒzzy + hzxy + zx(hy + hzzy) and           Nx = gx + gzzx + hzyx + zy(hx + hzzx).

Q: Explain why the function is differentiable at the given point. Then find the linearization L(x, y)…

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Q: Find the directional derivative of f(x, y) = sin(x + 2y) at the point (3, 1) in the direction = 5/6.…

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Q: 12. r (t) = cos ti +2 sin tj (0) a. r b.r (7/4) С.г (0 — т) d.r (7/6+ At) -r (T/6)

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Q: Find the directional derivative of f at the given point in the direction indicated by the given…

A: For the directional derivative first find a unit vector in the direction of θ=π4 then take the the…

Q: Let f(x, y, z) = x“y + z* and x = s³, y = st°, and z = s°t. (a) Calculate the primary derivatives ,…

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Q: 2.31 Let A and B be vector functions of position vector x with continuous first and second…

A: Let A and B be vector functions of position vector x with continuous first and second derivatives,…

Q: 2. Show that e*, sin x, cos x are linearly independent using Wronskian Method.

A: As per the policy of bartleby the provisions is to solve only one question at a time  I am solving…

Q: Another derivative combination Let F = (f. g, h) and let u be a differentiable scalar-valued…

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Q: 2. Consider the vector-valued function R(t) with Ả(1) = (1,2,−1) and R'(t): = (17/3/7-2) a) Find…

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Q: Tove or disprove the following claims. et W, X, Y, ZCZ a) (W-X)- (Y – Z) = (W –Y)-(X-Z)

A: To Prove or Disporove (W-X)-(Y-Z)=(W-Y)-(X-Z)

Q: Img(:)=v(x.y) and g(-)=g: v(x, y) = 2x-2ry+sin xsly and g (0)=-1.

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Q: A Find the value of J G dL if G = x'a, - xyza, given points P,(1,2,3) and P;(5,0,4) and a path…

A: Given: G=x2ax-xyzaz P1:1,2,3 P2:5,0,4   To find: The value of ∫P1P2G·dL for a path consisting of:…

Q: estimate the error

A: According to our company policy we are supposed to answer only first question. For the rest please…

Q: Calculus of vector-valued functions: Calculate each of the following. d (r(t)), where r(t) = 3 cos²…

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Q: a red coin as a 1 on one side and a 3 on the other. a blue coin has a 0 and 1. let X represent the…

A: Given Red coin→ 1,3 Blue coin→ 0,1 X→ Total of both coins Y→ No. flipped on the blue coin

Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

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Q: Find the gradient of the functions below. a)f (x, y, z) = sin(xyz)

A: Here we will find out the required value.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.