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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 3…

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Q: Evaluate the line integral - -ydx + xdy along the curve C : y? = 3x from (3, 3) to (0,0). NOTE:…

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Q: dx

A: A detailed solution is given below.

Q: Determine the vector field of F. F(x, y) = yi - xj

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Q: A piece of wire 21 m long is cut into two pieces. One piece is bent into a square and the other is…

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 5ytx²j+4z² div F= curl F=

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Q: Complete the table. (Use C for the constant of integration.) Original Integral Rewrite Integrate…

A: We can evaluate the given integral by using the following formula.

Q: Use the function to find the image of v and the preimage of w. T(V,, V2) V2, 2v, v= (7, 7), w =…

A: In given problem we have to find the image of given vector 'v' and preimage of given vector 'w' .

Q: Q5. Kindly answer within 10 mins, thank you

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Q: Find the series' interval of convergence and, within this interval, the sum of the series as a…

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Q: 2. A turns 100 RPM and B 150 RPM as shown; they are connected by rolling cones. Calculate the cone…

A: Solution: wa = 100 rpm wb = 150 rpm

Q: Find the general solution of the equation. Express the solution explicitly as a function of the…

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Q: Use Newton's method with the specified initial approximation x, to find x3, the third approximation…

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Q: Suppose that f (x) is a function such that lim f(x) and lim f (r) both exist. r3+ Does this mean lim…

A: Use limit definition to prove the limit.

Q: Find V· (V × F) if F(x, y, z) = 9 sin xi + 5 cos(2x – 3y)j+ 7zk. - V·(V × F) %3D

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Q: Find each of the following limits. Since you use L'Hopitals Rule, explain why you use it lim 2?e…

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Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

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Q: Consider the indefinite integral le*+3 dx: a) This can be transformed into a basic integral by…

A: Explanation of the answer is as follows

Q: Evaluate the integral 7x sin y dy dx. 00 The value is (Type an exact answer, using x as needed.)

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Q: Ise Newton's method with the specified initial approximation x, to find x, the third approximation…

A: Solve the following

Q: Find the indefinite integral by using the substitution x = 8 tan(0). (Use C for the constant of…

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Q: Sketch the region enclosed by y = 4x and y = 7x². Decide whether to inte with respect to x or y.…

A: we have to find the area of the region .

Q: I have this math problem that I am very stuck on Suppose that a, b, and c are unknown constants such…

A: answer is in next step .please give a like.

Q: Define Euler's number e. Sketch the graphs of the function f(x) = at are the domains and the ranges…

A: answer is in next step

Q: Evaluate the following improper integrals. Tell whether it is convergent or divergent. dx

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Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: Here, the given surface is  6x2+y2-3z2=4⇒f(x,y,z)=6x2+y2-3z2-4 Let, P(x0,y0,z0) be the point of…

Q: Determine if the function is a solution to the given differential equation. y = x In x + 6x + 5; y"…

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Q: b) X, + X2 - 2 X3 +Xy = a) 5X +2y = 1 3X +2y %3D = 1 Xz - X3 +2 Xy = 1 %3D = 5 X - 5y = 6 c) 2x, +8…

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Q: Use partial fractions to evaluate the definite integral. Use a graphing utility to verify your…

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Q: Find dy/dx. x = Vt y = 9-t dy dx

A: Here, x=t3y=9-t

Q: Evaluate the definite integral

A: Given∫pi/40sin62wcos62wdw,

Q: Given a function f(x, y) = In(9 – x² – y²). (a) Find and sketch the domain of the function. (b) Find…

A: Given function f(x,y)=ln(9-x2-y2 )

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (V2 - V1, Vị + V2,…

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Q: tó úsé co ór -0o, enter INFINITY or -INFINITY, respectively.) (-1)" + 1n! 1. 8. 15 ... (7n + 1) n =…

A: Solve the following

Q: Evaluate. 1 6 x dx V16 +3x2 0. V19 A) B) 2/19 -8 C) V19 -4 - 2 D) -219 +8

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

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Q: Evaluate (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (5, -5)

A: The objective of the question is evaluate the definite integral.

Q: a) Prove If he Given DE Is exact or non-exact Find its General solution

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Q: Find the distance from the point to the plane. (5,7,6), 10y +z= 0 The distance is

A: We can find the distance as below.

Q: ​(A) Find the average value of the function over the indicated interval.   ​(B) Graph the function…

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Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We want (x,y,z) such that 6x2+y2-3z2=4 and ∇f(x,y,z)=λ(2i→+7j→-k→) for some λ where…

Q: Evaluate the line integral -ydx + xdy along the curve C: y? = 30x from (30, 30) to (0,0). NOTE:…

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Q: af(x, y) If f(x, y, z) = , then is equal to dz

A: Given,  f(x,y,z)=x-zy-z

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 5 cos(t)i…

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Q: Solve the initial value problem. 4 y(x) = 4 sec(3.x) tan(3.x) ; y(7) = %3D 3

A: y'(x) =4 sec(3x) tan(3x)y(x)=∫ 4 sec(3x) tan(3x) dx3x=t,dx=dt3y(x)=43∫ sec(t) tan(t) dt     =43 sect…

Q: dr 5. 2 ?+3 2

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Q: 4. a = 20 m [W 30°S] b = 30 m [W 40°N]. Find a - b. %3D %3D

A: We need to find a-b.

Q: 4- if U(x,y) = x2 + 2y and x(r, t) = r sint, y(r,t) = sin?t, au find 1- ar au and 2- at au 1- ar ди…

A: Given that,   U(x,y) = x2+2y   and x(r,t) = rsint,     y(r,t) =sin2t we have to find ∂u∂r,    ∂u∂t…

Q: Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

A: The solution is given below.

Q: Find V· (V × F), if F(x, y, z) = 3ei+ 4.xe®j – 2ev²k. V·(V × F) =

A: We need to find dot product.