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 independent of path in R° and use a potential function to evaluate the integral.

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Q: find dy/dx

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Q: x3 dx (x – 1)5 y = Select one:

A: First evaluate the integral by substitute method. Then apply the limits of integral.

Q: Find a potential function for F. f(x,y,z) =

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Q: What is frz, fyy, and fyz of f(x, y) = In(y²")?

A: Given:           f(x,y)=lnyx2          fx=∂∂xlnyx2         Treating y as constant variable…

Q: 4. Compute the first fundamental form.

A: Given xu,v=u2-cosv,u+sint, cosv

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Q: Compute dy/dx using chain rule where y = (u^2+2u)/(u+1) and u = x(x + 1)

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Q: Compute (S ,g) where f(t)=1– 3r² , g(1)=t-ť'onV = C[0,1]. %3D

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Q: Sketch the slope field and solution curves   a) yy' + 4x = 0, (1,1), (0,2)

A: The given equation is yy'+4x=0 for 1, 1 and 0, 2. To find: sketch the slope field and solution…

Q: Find a potential function for F(x, y, z) = :yi+xj+xzk or prove none exists.

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Q: le can define an operator * : 2'(R?) n'(R?) by defining *dx = dy and *dy = -dx, and extending…

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Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(x+y) * (xy-1).

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Q: Find of / dx and of / dy. f(x,y) = e(x+ y + 9) of / dx = df / dy =

A: Let f be a function of x and y. The expression ∂f∂x implies that partial derivative of f with…

Q: Find the work done by F(x, y) = (x, Y) over the curve r(t) = (e' cost, e' sin t) (x² + y?)3/2 from…

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Q: dx Cane:2e-25x

A: 13)

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: Calculate Vf, V•f, V×f f (x,y. =)= xi+ y'j-* by the function

A: Introduction: The curl of the vector f(x,y,z)=fxi+fyj+fzk is given by ∇×f=∂∂xi+∂∂yj+∂∂zk×fxi+fyj+fzk…

Q: find ow/ar if w = (x + y + z)², ar www w x = r – s, y = cos(r + s), z = sin(r + s) at the point (r,…

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Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(xe^y) .

A: Solution:

Q: Find the potential function for F(x,y,z) = (x^-1z)i + (y^-1z)j + ln(xy)k. Show all steps and explain

A: Potential function of  F, is f such that ∇f=F.

Q: Find the Fourier integral that represents the following function   f(t) =e^−t+e^−2t  ,    t >0.

A: The given function is,f(t)=e-t+e-2t, t>0

Q: 6. Let z = 5e** sin y . Compute the differential dz. A) dz = 20et* sin y dx + 20e** cos y dy B) dz =…

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Q: 5. Compute the lenght of the curve u = t, v=0 from t = 0 to t = 1 using the first fundamental form.

A: Suppose, a continuous function is provided over a certain interval. The arc length is the length…

Q: Find the quadratic approximation at (0,0) for f(x,y) = ln(1+x^2 + y^2).

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Q: Solve X' Uxx - Y Uyy = 0 x,y>0 also find its canonical form

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Q: Integrate f(x, y) = 2x over curve C given that C is the part of y = 2x^2 from (2, 8) to (

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Q: Can someone help me explain why my teacher mutiplied the equation by (x^4)' in step 2? I thought I'm…

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Q: = (u² - cos v, u + sint, cos v) x(u, v):

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Q: dr [(2 = 1) A (Vy (y # a) (y? +1))1 O True O False Brief explanation:

A: Given statement is, ∃xx2=1∧∀y(y≠x)→(y2≠1) The equivalent statement is, There exist an x such that,…

Q: show y=3x+cos3x is a particular integral to d^2y/dx^2 + 3dy/dx +2y = 6x-7cos3x-9sin3x+9

A: To show: y(x)=3x+cos3x is a particular integral to d2ydx2+3dydx+2y=6x-7cos3x-9sin3x+9.