Compute fe F d where F (x, y) = x² + y). (2xy + x, Hint: Is F conservative?

Q: f(x,y) = =dt V11-6t?

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Q: Find the most general antiderivative of f(x) = Vx(x-x). %3D

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Q: The joint PDF of X and Y is given as S2, 0< x< y<1 f(x,y) (0, otherwise

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Q: Let f(x) = Va (2 – x)2. Use the local linear approximation of f (x) at ro V0.99 (1.01)?. 1 to…

A: To use the linear approximation for the given function

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A: Use the linear approximation of f(x)=1/(1+x) at x=0 to approximate f(-0.1).

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Q: Find fr and fy- S(x, y) = /"9e" dt f.(r, y) : %3D f,(x, y) =

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Q: Let f(x) = esinx and x(t) = t2. Calculate at t = Vn. %3D dt

A: Given:           f(x)=esinx and xt =t2        dfdt=dfdx·dxdt     f(x)=esinx      Derivating the…

Q: d) Evaluate using integration by parts: J(x+ 2)In x dx

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Q: (Xy,Z)%3Dex(cosy +sinz) fr?, fy =?

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Q: Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ] 3

A: Solution: The objective is to find the linear approximation

Q: Consider the function f(x) = 3z10 + 3z° – 3z² – 4. Enter the general antiderivative of f(z)

A: Given function is : f(x)=3x10+3x5-3x2-4 We have to find antiderivative(integral) of the given…

Q: Use the linear approximation of f(x, y) = eX +y_ at (1, 2) to estimate f(1.01, 1.98). (Round your…

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Q: Let F(x) be an antiderivative of f(x). If F(1) = 12 and f (x) dx = 17, what is F(4)?

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Q: Show that the function y(x, dy/at = a2y/ar2 = dy/ax = %3D %3!

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The joint PDF of X and Y is fær(x, y) = {"e * 0sy<x] otherwise .

A: The joint PDF for X and Y is, fx,y=λ2e-λx, 0≤y&lt;x   Given that W=X-Y Let Y=V W+V=X Consider, the…

Q: Using the linear approximation of f (x, y) near (x, y) = (1, 0) tells us that f (0.98, 0.05) is…

A: The linear approximation of a function f(x, y) at (a, b) is L(x, y) = f(a, b) + fx(a, b)(x − a) +…

Q: 3. Given f(x,y) = xy + y2 +1° ey Verify that fry = fyx %3D

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Q: 3) f(t)=t cosh(at) Ans. F(s)= s' + a? %3D 5) f(t)= 2te' Ans. F(s)= (s-1) %D 2.

A: We find Laplace transform of given function

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Q: The linear approximation at x = and where B is: 0 to 1 X is A + Bx where A is:

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Q: Find fr and fy- f(x, y) = 7e dt f-(x, y) = f,(x, y) =

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Q: Find the total differential. z = 10x6y7 dz = %3D

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Q: Let f(x, y) = 6e sin(7y) af af dy

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Q: Integrate the function f (z) = (z – 8i)² from z = 0 to z = 4 + 4i along the line x = y. 2

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Q: Find fr and fy. 2e" dt f (x, y) = 2, f.(r, y) = f„,(x, y) =

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Q: Find fr and fy- f (x, y) = 4etlo dt f#(x, y) f„(x, y) =|

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Q: Let f(x, y) = 7e2" sin(5y) af af dy

A: We can make it easier for you

Q: of find 4x + 9y of and dy For the function f(x,y) = %3D of dx ||

A: We can answer this question as below

Q: Let f(x, y) = 3e" sin(5y) af af dy

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Q: Find fr and fy. f (x, y) = 4e" dt f(x, y) = f,(x, y) =

A: A detailed solution is given below.

Q: 2. Let F(x) = re* %3D VE dt, find F'(x). t2+sint

A: Solution is given below:

Q: Find He valve of fe2) when fg functions such that are dilferentrable %3D g(x) >o 1 for all x, while…

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Q: Disccus the hatural of the Critical points: f(x,y) = 3xy-x²-y?

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Q: find given f (x, y) = e² + 2xy² – 4y at (0,3) af dy'

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Q: Find fyy for f(x, y) = e* In(y).

A: The given function is fx,y=exlny.

Q: he The product of linear integration is where c t $ (2xy – x²) dx + (x + y²)dy, x = y? 30 y = x? ,…

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Q: b) f(x): 1 + sec2

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Q: r an antiderivative of f(x). Do not enter +cas ver: +c

A: topic:- integration

Q: [4xy + 2x] 5) Let F(x, y) =[ 2x² + 1 Is F conservative? If so, give a potential function for F. %3D

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: a. Apply the Runge-Kutta method of 4th order to find the approximate value of y for x =0.2, dy in…

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Q: Find the antiderivative F(x) of f(x) = 8(sec x)(sec x – 4 tan x).

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Q: Find the local linear approximation L (x)of the function f (x) = lnx at x = 1 %3D

A: LINEAR APPROXIMATION

Q: Find fr and fy- f(x, y) = fetlo dt f.(r, y) = fy(x, y)

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Q: f(x, y) = /32² + 3y fz(4, 5) = VT23 %3D

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Q: Consider the function f(x) = 4x° + 7x® – 9z³ – 10. %3D Enter the general antiderivative of f(æ)

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Q: Find f and fy- f (x, y) = 9e dt f (x, y) = %3D fy(x, y) =

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Q: 4) f(x,y) =Vx +y Ans. f.= +y Vx + y?

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