In Exercises 17-20, compute f x and fy. 17. f(x, y) = 2x + y 2              19. f(x, y) = sin(xy)e-x-y 18. f(x, y) = 4xy 3                   20. f(x, y) = ln(x 2 + xy 2)

Q: 3.2.10 Example: By method of contour integration, prove that dx = t /4 (1+ x }

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Q: 16. What is the derivative of f (x) = e8x+3? %3D a. f'(x) = e8 b. f'(x) = 3e8x c. f'(x) = 8e d.…

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Q: 9/ Verify that Way Wxy = Wyx %3D W = e +X Ln y +g Ln X

A: Given that : W=ex+x.lny+y.lnx Do derivative w.r.t 'x' , we get : Wx=ex+lny+yx Now, do the derivative…

Q: Let f(r, y, z) = ln(x² + z) + y²e#² – cos(2yz). Find fzyr- %3|

A: Consider,                                                                 f(x, y, z) = ln(x² + z) +…

Q: 5. Test the exactness of ODE, if not, use an integrating factor to make exact and then find general…

A: Differential equations

Q: the linearization of (fi,f2) = (x²y+ 3xy², 3x³ + 2xy) at (1,0) to approximate the value at…

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Q: Verify Young's Theorem y? x2 z = In(2x + y) + +e(x+2y) y

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Q: 23. Find the most general antiderivative of the functions: a) f(x) = 1 –- x³ + 5x5 – 3x7. 5 – 4.x3 +…

A: Given: 1.fx=1-x3+5x5-3x7 2.g(x)=5-4x3+3x6x6 we want to calculate the antiderivative is nothing but…

Q: 10. Find the linearization, L(x,y,z) of the function f (x, y, z) = e* + cos(y + z) at Po (0,",").

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Q: Oy" +3y + 2y = (1+x) (1 – ¤) O y" +3y +2y = 2 sin a cos r %3D (e +e =) 2y" +3y + 5y = %3D Oy" +2y +…

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Q: Verify Young's Theorem y? x2 z = In(2x + y) – + e(x+2y) + - y

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Q: 1) The substitution u = tanx gives∫(sec2x.tanx)dx = ∫(x)du = 1/2.u2 + C = 1/2.tan2x + CThe…

A: Yes, both integrations are correct by their respective substitutions.Reason:An integral of a…

Q: find ∇f at the given point. ƒ(x, y, z) = 2z3 - 3(x2 + y2)z + tan-1 xz, (1, 1, 1)

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Q: {[{ ال 1: تحق ق من دالة التالية تحق ق معادلة لابلاس :س Z = In /x2 + y² اضف ملف ك 3. fxy ل لدالة :…

A: To find  Partial derivatives of the given functions

Q: 23. Given that f(0) = v2 cos (e-), the minimum value of o1+ v2 C. %3D COS D.-1 A. V2-1. B.2N2

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: ) Find the linearization of f(x) = sinx at x = 0.(b) Compute dy if y = x2 +x and x changes from x =…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: uxx+uyy=0; u1(x,y)=cos x cosh y, u2(x,y)=ln(x2+y2)

A: Given:

Q: Recall the chain rule from differential calculus: f (g (æ)) = f' (9 (æ)) · g' (æ). d dx Find de tan…

A: We have to find

Q: 4y" + 24y' + 27y = 0 @y(Tt) = 1, y'(Tt) = 0* O y(x) = 6 [e^(3(t-T!)] cos(t/2) - e^(3(t-T1) sin(t/2)…

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Q: In integrating the function fx* in Sx dx using integration by parts, what would you choose for your…

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Q: (b) f(x, y) = 3.03 + 3y2 – 4 ln y, a = 0, y = 1, dr = 0.01, dy = -0.01. since fa (x, y) = 3.3x-1+ 0…

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Q: Let f(x, y, z) = ln(x² + z) + y²e#z – cos(2yz). Find fzya.

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Q: In Exercises 55–60, verify that wy = Wyx- 55. w = In (2x + 3y) 56. w = e* + x In y + y ln x 57. w =…

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

Q: - Find the total differential df of f (x, y) = (x² + y²) 3/2.

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Q: Find the linearization of the function f (x)= x³ at x = 1. qb |a| sin (a) L (x) = Using this…

A: Given, fx=x5 We know that, If we have a differentiable function f defined near "a" the linearization…

Q: Let f (x, y, z) = ln(x2 + z) + y2 exz. Find fzyx

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Q: 5 The function f (x, y) =| x² cos² is homogenous in x and y of degree,

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Q: Mixed Partial DerivativesIn Exercises 55–60, verify that

A: (Note: We are entitled to solve only 1 question at a time). Given: w=ln2x+3y To Verify: wxy=wyx…

Q: 10. Find the most general antiderivative; verify your answer by differentiation. 5-4x 2x" b) f(x)…

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Q: 1. Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1,2).

A: Given triangular region is bound by the vertices 0,0, 1,0 and 1,2. The sides of the given triangular…

Q: 19. Let f(x, y, z) = + sin(3z) + e"-2". Find the rate at which f is changing at (2, 4,0) in the…

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Q: Verify Young's Theorem S. f(x, y) = = e(2x+y) In(xy)

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Q: If e**У- ху, then dx x(1- y) A Ax- 1) Ax - 1) B x(y- 1) (1- x) x(y- 1) x(y- 1) (D Ax - 1)

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Q: At what points (x, y) in the plane are the functions in Exercises 31–34 continuous?

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

Q: Let z(x, y) be the function implicitly defined as the solution to 2x + y + z + sin(xyz) = 4 + that…

A: ddxsinnx =cosnxddxnx =ncosnx

Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

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Q: Suppose f(x, y)= g(x)h(y), where g and h are continuously differentiable functions of one variable…

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Q: In Exercises 23–26, find ƒx , ƒy , and ƒz . 23. ƒ(x, y, z) = e^-(x2+y2+z2) 24. ƒ(x, y, z) = e^(-xyz)…

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Q: A) F(x,y) = (cos(x+ y) – y sin(x + y), –x sin(x + y)) 1 2т — у B) F(x, y) = ( - x – y’ xy – y² C)…

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Q: In Exercises 31-42. find dy/dx. 31. y = x4 33. y = Vx 35. у %3D (2х + 5)-12-( 32. y =x-3/5 34. у Vx…

A: 31 . y=x9/4

Q: 15- dy _y* -x diferansiyel denkleminin genel çözümü aşağıdakilerden hangisidir? 2ху dx x-y' =cx 046…

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Q: x²y" + 3xy = 2 O -y

A: see below the answer option (d) is correct

Q: If f(x.v)= e-2x° cos(5x +y),- af dy O a. e-2[4xcos(5x +y) + sin(5x + y)] O b. -e-2x[4xycos(5x + y) +…

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Q: 4] I Let w = 5 cos(xy) – sin(xz); x = 1/t, y = t, z = dw using an appropriate form of the chain…

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Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

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Q: Verify Young's Theorem z = In(2x + y) y? x2 +e(x+2y) y

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Q: 6. If z2 = x2y2 (where x, y, and z are positive), and dz then what is when x = 2 and y = 3, given…

A: Given problem:- If z2 = x2 y2 (where x, y, and z are positive), and dz/dt then what is when x = 2…

Q: -f(x,y, z) = 2z3 – 3(x² + y²)z + tan-1 xz , (1,1,1)

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Q: In Exercises 23–25, find ƒx , ƒy , and ƒz . 23. ƒ(x, y, z) = sec-1 (x + yz) 24. ƒ(x, y, z) = ln (x +…

A: We’ll answer the 23rd question since we answer only one question at a time. Please submit a new…