Let f(x, y) = x2 + y² and x = u2cos(v), y= u²sin(v). Then af at the point where u = -1 and v=0 is ди O A 4 O B. -4 OC. 0 O D. None of these

Q: 4. Let w = f (z) = 2iz + 67, find u and y and the value of f at z =+ 4i %3D %3D Z ==+

A: We need to find u, v and value of f at z.

Q: (b) f(x) = where A; E S™ – (det(Ao + x1A1 + ...+ xn An))/m, on {x | Ao + ¤1A1 ++xnAn > ► 0},

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Q: The function f(z) =e² is: u(x.y)=e*cos(y) o u(x,y) =e*sin(y) ¤ contiuous in СО discontiuous in CO

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Q: Iffis of class c? and z= f(y.x), con u= x°y°,v = 5x+1. Verify that| :4xy kxy+ 4x³y° + 10xy- af дхду…

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Q: Compute DF(, ) of F(1, y) = (e" cos(ry), r² + y) %3D

A: Given function is F(x,y)=eycos(xy), x2+y Let  f1(x, y)=eycos(xy)f2(x, y)=x2+y

Q: Let F (r, y, z) = sin y i+r cos yj- sin z k.

A: Given,        F(x, y, z)=sinyi+xcosyj-sinzk.

Q: Let /:R'R. S(x. y.2) = (e' tan y,x' In y). Compute D(f).

A:

Q: Consider the functions z =2e* In y, x In (u cos v), and y= u sin v. dz (a) Express and du dz as…

A: Since you have posted a question with multiple sub-parts, we will solve first two subparts for you.…

Q: Ql: Let f(x, y) = x + y,0 < x < 1,0 < y < 1. Find fi (x), f2(y), Cov (X,Y).

A: As per our guidelines we are suppose to do only one question  Given function isf(x+y)=x+y ;…

Q: Let f(z) = sin(3z) and C: |z| = 1. Then ſ. f(z)dz = z2(z-n)

A: In this question, we have to find the value of the complex integral by using the residue theorem.

Q: 13. If y (x, t) is a function of x and t, prove that i) L. =py (x, p) – y (x, 0) 2. ii) L =p°y (x,…

A: By Bartleby policy I have to solve first 3 subparts

Q: Let f(r, y, 2) = e tan(r*z²). Compute fry: (r, y, z) . Simplify your final answer. %3D

A: We will find out the required value.

Q: Let f be a differentiable function of one variable, and let f(p), where p = (x² + y² + z²)'/2. Show…

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Q: Find fr and fy- pry S(27, y) = /" 2e" dt %3D f.(r, y) = | f„(x, y) = | %3D

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Q: Given function f(x,y,z)=2x+ y+xz_where OSxS4, 0sys7 and 1szs5. Evaluate f(x,y,z) dV. V

A: The triple integral ∭Vfx, y, z can also be written as ∫ab∫cd∫effx, y, z dx dy dz, where e≤x≤f, c≤y≤d…

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

A:

Q: Consider the functions z=7 ex In y, x= In (u cos v), and y= u sin v. dz dz (a) Express and as…

A: Given, z= 7 ex ln y    ....... (1)x= ln ( u cosv) .......... (2)y= u sinv…

Q: 6. Let f(r, y, z) = e=² cosh y + z ar ff at the point P in the direction of :

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Q: Suppose f(r) z2 + sin z and F is an antiderivative of f that sausfies F(T) 0. Then F(2) = ( -1)

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Q: Let f(x, y, z) = e tan(x°z²). Compute fryz (T, Y, z). Simplify your final answer.

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Q: O Find all second order derivati ves for f(x,y) = Cos(2x) - x²e5Y + + 3y2

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Q: Let F(x, y) = G , y 1 )- Calculate the work against F required to move an object from (1, 1) to (3,…

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Q: Suppose f(z) = r + sin z and F is an antiderivative of f that satisfies F(#) = 0. Then F(z) =

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Q: If f =x-e" and F=x'yi-2y'zj + xy'z'k, find: div(F x grad(yf )) at (4,1,-2)

A: The function                     Then, we have to find

Q: of Let f(x,y) = xy° +7. Evaluate at (x,y) = (-7,1) and interpret the results. ду -

A: In this question we have find δfδy at (x, y)=(-7, 1)

Q: H.W: Find fr, fyand f if f(x,y, z) = x-Vy +z

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Q: a²f If f(x,y) = e" sin (r + y), then prove that дхду дудх %3D

A: Hi! You have posted two non-related subparts. As nothing is specified, we are answering only the…

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

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

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Q: Let T = x²y-xy³ +2; x=rcos0, y=rsin 0. Find and OT at or 20 TAT

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

A: We can make it easier for you

Q: Evaluate / f(z)dz when ) f(z) z+1 and y = TR (R > 0) z2 (ii) f(z) = (z+1)³ sin(z2022) and y = r(0;…

A: Given function i fz=z+1z2 and γ=ΓRR&gt;0iifz=z+15sinz2022 and γ=γ0;1

Q: Q = find of るf and るこ for the Ganction f(xz)-ディズ メ+Z

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Q: Let f(x, y) = xcosy - ye*y. fry at (1,0)is equal to: -1

A: See the attachment

Q: (a) Let f(r, y) = x - 3ry + 18y, where 3r?y- y- 6x = 0. Prove that f(r, y) has extrema at the points…

A: Calculate partial derivative of f(x,y) with respect to x and y ,

Q: Let f(x, y) = y cos (xy), then f.(x, y) = fy(x, y).

A:

Q: c) Let f(x, y,z) = cos (xyz)sin(x²y=

A: The given function is f(x,y,z)=cos2(xyz)sin(x2y2z2) ..............(1) we have to find;  fx=∂f∂x=?and…

Q: Suppos analyts s? show work. you

A: Given that f is analytic. And z≤1 And f(0)=0 And f(5)≤5 The formula for derivative is,…

Q: Given f(z, y) = 7x° cos (y*), find fzy(z, y) = | fyy(T, y) = [

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Q: If y (x, t) is a function of x and t, prove that i) Lat =py (x, p)- y (x, 0) ii) L- = p°y (x, p) –…

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Q: Let f(x,y) = xcosy – ye*y. fry at (1,0)is equal to: -1 -5

A: fx is partial derivative with respect to x fy is partial derivative with respect to y

Q: Let f (x,y) = sin(xy) + x² ln(y). fyx at (0,) is equal to: %3D А. 33 В. О С. 3 D. 1

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Q: 44. Let f(x, y) = g(u), where u = x² + y² and g(u) is differentiable. Prove that 2 4u (dg Әх du

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Q: If f(x, y) = x cos y + ye", find the second-order derivatives %3D af a²f ах ду" and ar" dy ax'

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Q: II. Let f(x, y, z) = z° sin a + Determine 2 dydzərəz'

A: We know, ∂2f∂y∂x=∂∂y∂f∂x

Q: f(z) dz where a inside r= z-a

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Q: If f(z) = sin(z 2) = U(x, y) + iV (x, y), determine U and V . Verify that the C-R conditions are met…

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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: Let f (x, y) = x+ y Evaluate . f (x,y)ds when x sin t, y = sin t

A: Explanation of the solution is given below...

Q: Let f(x, y) = Vje». Find 1. frx 2. fyy 3. fry

A: Please find the solution in the attached images :

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.