Determine frx and fry for the function below: f (x, y) = x²y + y cos x – e*y In((y) + 7. -

Q: Consider the one-form y4 W = dæ + (4 ln(10x)y³ + 13y) dy on {(x, y) E R² | x > 0}. If the one-form…

A: Given: The one-form…

Q: A) Use the chain rule to find where w'sy',x= sint + cost y = cost - sint. B) If f(x. y) - xy?+ x'y ,…

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Q: the most general antiderivative function Find f(e) Sx-4+3x %3D t has

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Q: The antiderivative of the function f(z) = + 10z is

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Q: Consider the function f(t) = 3 sec²(t) - 3t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

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Q: Consider the function f(x, y) = 3 x² y + cos(e*'). Which one of the following is correct- Oyf x-x…

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

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Q: Given f(z) = | t2 – 16 dt 1+ cos²(t) OS At what value of a does the local max of f(x) occur?

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Q: Let x = x(t), y = y(t) and z = z(t). Differentiate the following function with respect to t. 2°…

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Q: Find the most general antiderivative F(r) of the function f(x) in each part: a) f(r) = 12r3 +4VT- e…

A: To evaluate antiderivative F(x) of the function f(x)=12x5+4x-ex+1 We know that∫xndx =xn+1n+1 +C ;…

Q: For the function f(x,y,z) = In (5x + 7y + 1Oz), find f,, f, and f,.

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Q: Find a non-zero function h for which F(x, y) = h(x)(x sin y + y cos y)i + h(x)(x cosy – y sin y)j is…

A: Given vector field is, Fx,y→=hxxsiny+ycosyi+hxxcosy-ysinyj.

Q: Let f(x, y)= Jxy +x+xcos y. (a) Find fy - ở² f_ (b) Find дхду

A: f(x,y)=xy+x+x cos y

Q: f(2) = | : t2 – 1 dt 1+ cos² (t) At what value of ¤| does the local max of f(x) occur?

A: Given that a function f(x) and we find value of x does the local maxima of f(x) occurred. We know…

Q: \+etari), find f.. S, and f.- xyz 3. If f(x,y,z)= hn 2

A: We have to find fx , fy , fz.

Q: Determine fzz, fyy, and fz for f(x,y,z) = x²y³z – y sin(xz) + e».

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Find dz/dr if z as a two variables function in r and y is defined implicitly by y3 + x22 + r sin r…

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

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Q: Consider the function 23 – 3y if (x, y) # (0,0), f (x, y) = x² + y? if (x, y) = (0,0). Show that…

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Q: Find an antiderivative F(x) of the function f(x)%3D7sinx/12+cosx such that F(0)=1

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Q: For ey – In x=y2, find the value of so that & (y' – y') = 1 at y =0- O e e

A: we have to find

Q: Find PSD of Y (i) interms of X (1). Assume O is independent of X (f).

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Q: The harmonic function for f(z) = u(x,y) + iv(x,y) to be analytic are:

A: Given that: f=u+iv

Q: dy for the following implicit function at p(1,1) Find dx Vxy +1 = y is O 1 O 1/2 O -1/2

A: A detailed solution is given below.

Q: i f(t) is given E ue of f(0.5) is

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Q: Q10. Expand f (x, y) = e" cosx about up to third degree terms by using Taylor's theorem for a…

A: The given problem is to find the third degree taylor polynomial of given function f(x,y) about point…

Q: dw at t= dt For the functions w = - 4x + 10y, x= cos t, and y = sin t, express as a function of t,…

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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: The function f(z) = 1 has a poles at z = %3| ez – 1

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Q: The function f(z) =e² is: contiuous in C discontiuous in C Ou(x,y) =e*cos(y) Ou(x,y) =e*sin(y)

A: The function f(z)=ez the given function is continuous.

Q: Assuming 9x° – 5y - 4xy = 0 defines y as a differentiable function of x, use the theorem dx - to…

A: Given: 9x3-5y2-4xy=0 We have to calculate dydx(1,1) by the given formula.

Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A: w=x2+y2+z2,  x=cost,  y=sint,  z=et a).…

Q: Q3) For f(x,y) = Sin(x,y) find fryxy at (1,–). %3D

A: Given query is to perform indicated derivative operation.

Q: Given a function f(x, y, z) = cos (x + xy²z²), find: f#(5,1, 1) = frz (T, 1, 1) = %3D

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Q: Find f. (Use C for the constant of the first antiderivative, D for the con f'(t) = Vt - 6 cos(t)

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Q: Given f(x, y) = y ln(5x 6y), find f-(x, y) = fy(x, y) =

A: The function is given by fx,y = yln5x-6y To evaluate : The expression of fxx,y and fyx,y.

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

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Q: Given F(x, y) = (sin y + e*, x cos y) and C: x=t, y=t(3 —t), 0≤t≤ 3. (a) Show that F is conservative…

A: Given : F(x,y)=sin y+ex,xcosy C:x=t, y=t(3-t), 0≤t≤3. To show:  (a) F is conservative and find a…

Q: Find fa, fy, and fz. f (x, y, z) = z In (x'y cos(22)) 5.4 fy = fz =

A: topic - partial differentiation

Q: Evaluate the given function using homogeneous y²dy = x(xdy – ydx)ey A. tn ) = 20* (1 –) 2e (1 - А.…

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Q: F(x,y)= (y² – 2x) i + 2xyj is conservative or not. If it is find a function f such that F = Vƒ.

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Q: Find an antiderivative F(x) of the function f(x)= 7sinx / 12+cosx such that F(0)=1.

A: Now,

Q: H.W:- Prave.that.he.Maclaurinsevi.of.f(x).=-C0JA 3. (い (2n)! 2 i 5... f.(x)..co3.X.1. メ n=0

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Q: The function f(x,y) is homogeneous of degree one. cos a) True b) False.

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Q: Consider the function f(x, y) = 3 x² y + cos(e*"). Which one of the following is correct- Oyfx-x…

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Q: e3x-y 2yx = t° In s , y = sin(ts). Find az Let function z x2y as

A: To solve the following

Q: Find the general sebution of the oDE dy Sin(x+y)+ Cos (X+y) %3D dx

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Q: The function f(z)=e² is: „(x.y) =e*sin(y) O contiuous in CO u(x.y) =e*cos(y) O discontiuous in CO

A: Use the property of complex function to break in real and imaginary part. Here also use the concept…

Q: f(æ) = / t2 – 9 dt 1+ cos? (t) At what value of x does the local max of f(x) occur?

A: Given: For the local maximum value of f(x), we must have f'(x) = 0. Here,…