Find the second-order Taylor approximation for f(x,y) = 1/(xy) at (1,2).

Q: Show that [ xdhy – ydy c Vx*+y² is independent of any path of integration which does not pass…

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Q: Evaluate L 8y (x³ + 1)² 2y by reversing the order of integration. dady

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Q: dz Z 1. around unit circle of radius 1 and center at (0, 0) counterclockwise. 2. By using direct…

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Q: Suppose that (z, y) = e-v and o(In 2, In 2) = 1. Please use the technique of %3D linear…

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Q: Show that (2x In yz-5ye") dx-(5e* -x²y)dy +(x²z- +2=) dz, where C runs from (2,1,1) to (3,1,e), is…

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Q: In 3 xp; J(1-x)*dx

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Q: Suppose that (r, y) = e-v and o(In 2, In 2) = 1. Please use the technique of linear approximation to…

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Q: 70. Solid bounded above by x² + y² + z² = 36 and below by = 2 Vx + y?

A: Given: Consider The volume of any solid E in R3

Q: Q5A) Find volume of body from above Z = √√4x² - y² and below Z - Triple integration. 1 using

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Q: dx (1 – e²)² -1

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Q: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Ay ~

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Q: Use Runge-Kutta's (4th order) method with a step size h=0.3 to intagrate the function y'=xy2-2xy…

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Q: Find the line integral of F along the parabola y = x² from the origin to (4, 16).

A: Using green's theorem.

Q: Calculate the order of the local truncation error of the Crank-Nicolson method for approximating the…

A: The heat equation given is as follows: ∂u∂t-∂2u∂x2=0 We are asked to find the order of the local…

Q: Find the total differential of the following: 1. f(x, y,z) =-tan'(x + y +z)+ In(xyz)

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Q: Evaulate the line integral of c (x^2+y^2) where c is the line segment from (-1,-1) to (2,2)

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Q: Find the local linear approximation of f(x) = In(5 + x) at xo = -4. %3D In(5 + x)

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Q: Find the second-order Taylor approximation for f(x,y) = exp[-x]sin[y] at (2,0).

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [(x + 3x²) dy

A: To evaluate: ∫C(x+3y2)dy...(1) where C is given by x=2t, y=4t⇒dy=4dt and 0≤t≤1

Q: Compute the line integral of f(x)=2x over the curve y=x² from (0,0) to (1,1). |

A: The line integral of f(x)=2x over the curve y=x2 from (0,0) to (1,1)

Q: 3. ) Compute for the increment of the function f(x,y) = *+3y . Also, find the total differential of…

A: w = f (x, y) and let ∆x and ∆y be increments of x and y respectively. The increment ∆w of w = f (x,…

Q: is the follecing dif Mantial opuatíon Jmeo on mot Y with x>1. ey-x

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Q: Find an integrating factor to obtain the integral curve of (2ау — 16х) da + dy 3 0 that pass -…

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Q: If F(z)dz f(t)dt, what are the bounds of integration for the first integral? and

A: Given  ∫abfxdx=∫−8−1fxdx+∫−11fxdx−∫−8−5ftdt

Q: Compute the 1st and 2nd degree Taylor polynomials L(r, y) and Q(r, y) for f(1, y) = In(r +y?) at…

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Q: 1- f(x, y) dy dx •x+1 f(x, y) dy dx + at is the sum of the four resulting limits of integration? 3.

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Q: Calculate the order of the local truncation error of the Crank-Nicolson method for approximating the…

A: We are given the heat equation as ∂u∂t-∂2u∂x2=0. Now, we will be approximating the heat equation by…

Q: Use the local linear approximation of (1 – x)2º at xo O to estimate (0.99)2º. %3D

A: The linear approximation of f(x) at x0 is given by L(x) = f(x0) + f'(x0) (x-x0)

Q: What is the value of the line integral ∫AB xy dx defined by the line y = x +2 and it is along the…

A: The given problem is to evaluate the line integral along the path y=x+2 from points A(0,2) and…

Q: Verify the condition of integrability for the given total differential equatior (3x*y2 – e*z)dx +…

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Q: Q3: Evaluate the integral f xe dx by first finding the Maclaurin approximation to the integrand with…

A: The Maclaurin series: fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+… Where centered at a=0 or x=0. Given:…

Q: A square is expanding in such a way that its diagonal is increasing at the rate of 2 in/s. (a) At…

A: GIven,  a square is expanding in such a way that its diagonal is increasing             at the rate…

Q: Evaluate. (use C for aonstant of intgration) dx 2 X "- 3

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Q: Evaluate the improper intergal dx using the residue 2 (x² + 4)² theorem.

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Q: Compute the path integral of F = ⟨ y , x ⟩ along the line segment starting at    ( 1 , 0 ) and…

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Q: S f(x.y)dxdy- Reverse the order of integration in 0,

A: The given integral is: To find the reverse order of integration.

Q: Find the partial integral. Y dy

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Q: 2) Find the total differential dz for z = tanhy In(x)

A: Total differential of z is given by dz=(∂z/∂x)dx+(∂z/∂y)dy

Q: dy J y3-2y2 у3-2у?

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Q: xcosr (i) Find the Cauchy principal value of the integral dr. ² + 4x + 8

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: What is the Laplace transform of the convolution integral of h (t) = sinh 3t u (t), x (t) = cosh(3t)…

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Q: Show that {zn}nEN is Cauchy, where z, = sint dt. 1+t

A: Sol

Q: Find any value of c for which the improper integral cx + 36 x2 + 1 9. da x (4 x + 5) converges.

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Q: Find the partial integral. (3х + 5y) dx

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Q: 4. Find the total differential of z = In(x + y), x= w, y = w². By how much will z change if w…

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Q: Find the antiderivative of f(x) = point (0,3). O F(x) = tan¹x +1 O F(x) = 2 tan ¹x +1 -1 O F(x) =…

A: Given: fx=24x2+1 and x,Fx=0,3   As we know the expression for the antiderivative; Fx=∫fxdx And…