Q,3 Evaluate [II, xyz dxdydz, 3 < x S-2,0 < y S 1,0 S zs-

Q: The standard form of 3dy – xydx = 3y³e¹x/³ by Bernoulli's equation is: dx A d 2=3e dy ху B D…

A: Solution : Given that

Q: 24. Evaluate x² dx + yz dy + (y²/2) dz along the line segment C joining (0, 0, 0) to (0, 3, 4).

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Q: 2x :S dr f(x, y) dy. f (x, y) dy. •1-x² f (x, y) dy. -V1-r

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Q: dy If y=/xsec 1(x²), then dx Select one: 1 sec 1(x?)+ 2/x 2 1 O b. sec 1(x)+ 2x x²Vx+ -1 1 2x Ос.…

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Q: . Zydx – (x – y)dy = 0, when x = 4, y = 4 O x- y = VI o x+y = 4/y o x+ 4y = V O x-Jy

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Q: y" - 3y' =f(t), y(0) = 1, y'(0) - 1 %3D 8 Given L{f(t)}= S-2 2 S+1

A: Given initial value problem is y''−3y'=ft, y0=1,y'0=−1 And given Lft=8s−2−2s+1 We know that…

Q: f(x, y) = /2x – y /2х — у f(x, y) = In(9 – x² – 9y²) f(x, y) = /1 – x²? - VI – y² S(x, y) = Vy + /25…

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Q: dy (2) Find at x =-1 if y = u³ + 5u – 4 and u = x2 + x dx

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Q: Let y = x2 – 4.x. With x = 5 and Ax = 1, find the values of Ay and dy. %3D %3D -

A: y=x2-4x , x=5 and ∆x=1

Q: Y = w tan-1(uv), u = r + s, V = s + t, w = t + r when r = -1, s = 2, t = -1 1. as at ar as %3D

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Q: 2, 0 1

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Q: Q1 If f(x,y, z) = 2 x²y + ez+ Vz Inx %3D Find fr fy and f2

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Q: 3. 다음 함수 /에 대하여 /w, /w 를 각각 구하고 비교하 여라. (1) f(x, y) = sin' xcosy (2) S(x, y) = 2x²+5xy+ y² %3D (3)…

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Q: If f(0) = 0 and f'(x) E (0, 1]Vz E [0, 1] then ( red) %3D can not take values S(=)*dz

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Q: the constant 'c' such tha 5y)âz + (y – 3x)ây z)âz

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Q: Find if f(x,y) = y sin xy ax %3D az Find ax if yz – In z 4. = x + y 3.

A: Given that: f(x,y)=y.sin(xy)   NOTE: As per our answering guidelines, we can only answer 1 question…

Q: 36. Using the approximation dy dy h dr * Yn+1- y. and that dr 1, y = 2 when r 0. Then, y A h- 2 h+ 2…

A: Please see the answer below.

Q: 2. [f 5y ey dA, F- {(x, y): 0 s x s y?, 0 s ys 2} F

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Q: sen (y) 1² + 3y? 522 – f(x, y) 2y – z 1² + 2y? f(z, y) zy3 12 + 2y? f(x, y) f(z, y) z°(1 – cos(y))…

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Q: 2 3 tegral of the function xy d by x = 0, y = 0, z = C %3D %3D (2(5)

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Q: (d) S (1, y) = sin (2), (x, y) # (0,0) 0, (x, y) = (0,0) (e) , r + y # 0 7+y x² + y = 0 0, f (x, y)…

A: Limit of a function: A function f is said to tend to a limit l as a point x, y tends to the point…

Q: Y : k=0 y' + (2x + 1)y = 0, rrence relation. For k > 0,

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Q: 1. Given f(x, y) = x'+y* find and ôx dy ôxôy Oyôx

A: we are allow to solve one question at a time  thank you

Q: Find fæ, fy, and fz. 4.5 f (x, Y, z) = 4z In(x*y° cos(5z))

A: To find the partial derivatives with respect to x ,y ,z.

Q: 1 z = Vuv, u = 3xy + 2x2 + e"-Y Find zzy at x = 1, y = 1

A: Topic:- function

Q: (3) Let f(x, y) = 3+sin(x) 4y2+10 Find both fa(r, y) and fy(x, y).

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Q: dy + 2xy = f(x), y(0) = 4, where xp Sx, 0sx<< 1 f(x) lo, x 2 1 0 < x< 1 y = x 2 1

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Q: 10 if the equations f(x, y, z)= 0, g(x, y, z)=0 can be solved for y and z as differentiable…

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Q: * Q9 If y = cos(x + y)dx + (3y² + 2y + cos(x + y)) dy = 0, then M = cos(x + y), N = 3y² + 2y Ttue…

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Q: (8) Fs [ J" f (x, y) | бул 1 = d^Fs dyn proof (H⋅w-)

A: Introduction: A Fourier remodel (FT) is a mathematical remodel that decomposes capabilities relying…

Q: _1. y +1-2 dy, can be evaluated conveniently if we let y+1-2=t and dy = 4r(r +2)dt. %3!

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Q: 3 13. If x = u + v³ and y = uv – v² are solved for u and v in terms of x and y, evaluate ди ди dv dv…

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Q: 3. Obtain the Particular Solution when x = 4 and y = 1 (x+ y - 4)dx - (3x- y – 4)dy = 0 %3D

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Q: y' + 4y = e^(4t) %3D

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Q: Find L(y). / + 2x = 2 - x' = et (0) = x (0) = 0 -2 L (y) PL(y) = %3D s(s2 +2) 2s L (y) = %3D…

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Q: Using the approximation dy dy * Yn+1 - Y, and that dr 1, y = 2 dr h when r= 0. Then, y, = A h-2 h+2…

A: Use the approximation hdydxn≈yn+1-yn and that dydx=1, y=2 when x=0. Then y1=?

Q: 9. xy sin yz dV, where G is the rectangular box defined by the inequalities 0 <x< T, 0 < y< 1,0 < z…

A: Given information: The integral is ∬∫xysinyzdV and the region is bounded by the rectangular box…

Q: 3. Given: y = f (u) and u = g(x), find dy/dx: a) у%3D сos u, и%3D—х/3 b) y = tan u, u = 10x – 5 - с)…

A: Our aim is to find the derivative of the above expressions.

Q: [2xy + yz (i) F(x,y, z) = x2 + xz with domain R³. || xY

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

Q: f (x, y) = 4xy² + 5a°y fzy (1, 1) = hx

A: Given: - The function is, f(x,y)=4xy2+5x3y To find: - The value of fxy(1,1)=

Q: D. Find Az) = u(x, y) + iv(x, y) with u as given. Check for analyticity. (a) u= x/(x² + y³)

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Q: -0.08. Then evaluate dy for a=-3 and dz *+1 %3D Let y = dy = %3D

A: We have to find

Q: 1. f (x, y, z) = x° ỹ + 4z°y² – xyz + x² – Vz -

A: Given that: f(x, y, z)=x3y+4z3y2-xyz+x2-z53               NOTE: As per our answering guidelines, we…

Q: Lety = xz – x² + xz² – 1. Find d'y evaluated at x=2, z=2, dx=1, and | - dz=1.

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Q: 2R then the constants R TCX If f(x) Rsin .2 S,f' and f(x)dx and S are respectively.

A: Introduction :Here we have asked to find the value of R and S

Q: sin(r. r dr dy. Compute O y/3

A: To evaluate∫01∫y131sin(πx2)x2 dx dyx= y13y = x3

Q: Q1) Evaluate SSS, xyz dV, where Q = {(x, y, z): 0 < x < 2y, 0 < y < 1, 0 < z < x + y }.

A: Since you have asked multiple questions, we solve first question for you. For other question to be…

Q: – 4z) dV where E {(x, y, z) | 0 < y < 1,0 < x < y, 0 < z < x + y²} Evaluate + Y E

A: We just need to put the limits and then integrate as following

Q: © f(X,y) = x4 + 'onY -10 © w = x*y - 10yZ z³ + 43X – 7tan (4Y)

A: It is partial derivative