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

Q: If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't…

A: It's nothing to do with f(z)=u(x,y)+iv(x,y). Here z be complex independent variable. Hence , z could…

Q: 2 consider, Differentiate with respect to x', dy C」.2ス %3D de

A: From the image , two find a differential equation eliminating the constants from the given relation.…

Q: If f(x, y, z) = ln(xª + yl0 + 2³) + V (x10 + y8 + z4), then find fr, fy and f; at (1, 1, 1).

A: The given function is fx, y, z=lnx4+y10+z8+x10+y8+z4 and the given point is (1, 1, 1). Evaluate fx…

Q: Consider w = x² – y², where x = s cost and y = ssin t. Find u and hu using the Cha dw at ds Rule.

A:

Q: af dy %3D Y Given f(x, y) = 17x² sin y then 17x2 cos y O -34x cos Y O -17x² cos Y 34x cos Y II

A: The function is given by fx,y = 17x2siny To evaluate : The expression of ∂f∂y

Q: dz dz Calcula y dy z = x In(y) az = In(y) 1

A: Given : z = x ln( y ) To Find : ∂z∂x, ∂z∂ywe have given four options to determine the correct option…

Q: а. y' +y tanx %3D sесх + сosx b. 1 -/dx+x?dy)=0 (x² - y?) C. yy' – 2y? = e* С. d. 1 -(хdy - ydx)3D0…

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Q: 2. Show that the function u = e(xy) + VrY 4(y/x) provides the equation Pu = 0. dy? %3D -

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Q: Evaluate /// (x + y – 5z) dV Where - E = {(x, y, z) | - 6 < y < 0,0 < ¤ < y,0 < z < x + y²}

A: The given integral is: I=∫∫∫E(x+y-5z) dV where E=(x,y,z) | -6≤y≤0,  0≤x≤y,  0&lt;z&lt;x+y2

Q: D. f(x, y, z) = 1x + 10y + 8z Vf(x,y) =i+j+k E. f(x, y, z) = 1x² +10y² + 8₂² ▼ f(x, y, z) =i+j+k

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Q: b Let y = x²sin(y) + yeXy, where x = s + 2t and y = st dv when s (ii) dt = o and t =1 is [d]

A: Find your answer below

Q: dz 2. Given z = 4x2 + y²,x = sin t, y = t², find- %3D dt

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Q: y*dx-(ay + y° kty = 0 Let the substitution v=2; y=vx; dy=vdx+ xdv

A: Given differential equation is y2dx-(xy+y2)dy=0

Q: u + c. Evaluate So (2x- y)3e dx dy with y = v, x= u-

A: To evaluate ∫02∫y22+y22x−y3eydxdy with y=v, x=u+v2.

Q: If f(x, y) = 4x? – 8y, then the total differential of f at a = 1 and y = -2 is : O df = 8 dx – 32 dy…

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Q: Find fr, fy, and fz. f(r, y, 2) — вуzIn(4ry) fz fy f: =

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Q: Find fz(x,y) and fy(x, y) given f(r, y) = csc yArcsin(r²).

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Q: b) d²y + 5y = 2t, given that y = 0 and = 1 when t = 0 dt dy %3D dt2

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Q: dw If w = f(x,y,z) = In(x² +y² z?),x = cost y= sin t ,z = 4VE , then is : dt + ww.

A: Given  w = f(x,y,z) = ln(x2 + y2 + z2) x = cos(t) , y = sin(t) and z = 4t Substituting the values of…

Q: D eter mine Paricular volution ( 2xy)dy = (y²-x²)dy j x=I,y= -2

A: In this question we have to determine the particular solution.

Q: b) Given z = f(x -y, 2x - 2y, 3x – 3y). Show that dz dz 0. ду

A: The solution is given as

Q: C is given by x = t°, y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + x dy + y dz)

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Q: Compute 6. da dy dz x²+y² + z² where V = {(x, y, z) E R³ : 4 0, y > 0}. Sketch the solid.

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Q: If f(x, y) = 4x² – 6y², then the total differential of f at x = 1 and y = -2 is : O df = 24 dx + 8…

A: df=dx+dy (see step 2).

Q: Integrate f (x, y,₁20 = 2² +12y +7 over the cure given by z) r(t) - £²³₁ +3+²7 +6+² 1st ≤2 Xtm E.T…

A: Given That: f(x,y,z)=z2+12y+zr(t)=t3i+3t3k+6tk To  find : ∫cF·dr

Q: 4 J4- y ktx dy S[S( x, y) dA = [] 3 R 0 2- 2 2

A: Consider the given expression, ∬Rfx,ydA=∫04∫2-y24-yx2-x33dxdy This suggests that the region spans…

Q: Evnlunte: (а) (- xy) dydx (b) dr(x-) dy, where y, = Va? - x?

A:

Q: Find fr, fy and fz. f(x, y, z) = x – Vy² + z? |

A: Given f(x,y,z)=x-y2+z2. The objective is to find fx,fy and fz.

Q: Consider the finction f(x,y) = x² + xy – 5x – y+ 1. Then:

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Q: True or False: For an IVP dy/dx = f(x,y); y(a)=b, if f(x,y) is not continuous near (a,b), then its…

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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: dy (3) If y = | (t – 1)²dt for x > 0, then compute dz In z

A: fundamental calculus theorem 2 states that if f is continuous on [a, b], then  ∫abf(x)dx=F(b)-F(a)…

Q: Suppose x(t) and y(t) satisfy da = y? – 1 , dt dy = 2 – 2x. dt - - d (3x2 – 6x 0. + y³ – 3y) = Show…

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Q: d²s ds + dt 4t + 2cost where s = 0, ds/dt = 0, t= 0 dt2

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Q: Evaluate //| (x + y – 2z) dV where E = {(x, y, z) | - 2 < y < 0,0 < x < y, 0 < z < x + y²}

A: A detailed solution is given below.

Q: (ztan 2 +1) dx – x dy = 0

A:

Q: Find fr, fy, and fz. f(x, Y, z) = 4yz In(6ry) fz = fy = f: =

A: Given: f(x, y, z)=4yz ln(6xy)

Q: z = √xy, dz dt t², y = -t² then 2 2 2t²) =?

A: We have to choose the correct option from the given options according to the given information

Q: Find fr and fy- f (x, y) = | 5e dt %3| fa(x, y) = fy(x, y) =

A: We apply fundamental theorem of calculas and solve it.

Q: e.) ay dy t (x³liny-x) dy = 0 %3D

A: To find: The solution using Bernoulli's method. Given: The differential equation is 2ydx+x3 ln y-x…

Q: a. Apply the Runge-Kutta method of 4th order to find the approximate value of y for x =0.2, dy in…

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Q: dy dæ at x = 2 if y = 3x + 5 and dt Find - 2. %3D %3D - dt dy %3D dt

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Q: u2-1 Given y = dy and u = Vx2 + 2, find dx %3D u3+1

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Q: If y= V (x-1), find dy (Use rules, not a de finition ) Xp

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Q: D SS f(x,y,z) dV = f(x,y,z) dx dy dz

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Q: If f(x, y) = 2x2 – 9y, then the total differential of f at x = 1 and y = -2 is : O df = 4 dx - 36 dy…

A: Given: fx,y=2x2-9y2 To determine: The total differential of f at x=1 and y=-2.

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: 4) f(x,y) =Vx +y Ans. f.= +y Vx + y?

A: