R = {(x,y) E R ×x R : x > y} T = {(x, y) E R × R : x > y}. RoT.

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

A:

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…

A:

Q: Verify Young's Theorem y? x2 z = In(2x + y) + +e(x+2y) y

A:

Q: In Exercises 5-8, calculate the gradient.

A: Here given as

Q: xsin-1(x) is 1– x² If x =0.58 and y = 0.31, then value of C in the antiderivative of F(x) = %3D %3D…

A:

Q: 2, 0 1

A:

Q: Solve for the antiderivative of the function f(x) = C. *++3x + C A. ++9x+C B. 즉++9x +C D. 2x ++3x +…

A:

Q: 3xz dV where E: {(x, y, z) | 0 < r < 2, x < y < 2x, 0 < z < x + 3y} Evaluate E

A:

Q: y4) + 2y" + y = 0

A:

Q: (2y-x)(dy/dx) = 2x + y, given that y = 3 and  when x = 2 Homogeneous equations

A: Solve the following problem by substitution.

Q: valuate S S Se(3 – 4x)dV, whe e xy-plane defined by 0 < x s

A: To find: ∫∫∫E(3-4x) dV

Q: (* +y – 4z) dV where E = {(x, y, z) | 0 < y < 2, 0 < * < y, 0 < z < a +y?} Evaluate

A: ∫y=00∫x=0y∫z=0x+y2x+y-4z dz dx dy Now, ∫z=0x+y2x+y-4z dz =x+yz-2z2z=0x+y2 =x+yx+y2-2x+y22…

Q: valuate S. F · ds, where F(x, y, z) = (z, x, y) and c(t) = (t, t², t³), 0 < t < 1.

A: F(x,y,z)=(z,x,y)

Q: ( b) SI[ vzcos(x* µV where E = {(x, y, z) |0 < x < 1, 0 s y s.x, x S z 5 2x } E

A:

Q: What is the value of the line integral ∫ AB y dx + x dy, if x = 3*t, y = 4*t + 4 and 0 ≤ t ≤ 1?

A: I am solving this in step 2

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

A:

Q: Find the solution u(x, y) of u+sin(r) uy = y for z, y ER, u(x = 0, y) = 0.

A:

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: 2. Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation to approximate…

A: The objective is to find the linear approximation to hx=x4  at  x=2 Use the linear approximation to…

Q: 1. a- Find a result by using variable separation for ý=secy h- xy = x + y

A:

Q: f(x, y, z) = e-3zyz 三 fy = 三 ニ f.

A:

Q: Find y' and y". - in(x + V6+ x²) y = In( x + y' = y" %3D

A: Given

Q: x = s·t u = x² + y³ +z*, {y = s² +² z = s- t

A:

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = ln (x + 2y + 3z)

A: Given, ƒ(x, y, z) = ln (x + 2y + 3z)

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

A:

Q: xsin-(x) If x =0.03 and y = 0.62, then value of C in the antiderivative of F(x) = is V1-x2

A: Given  F(x) = x sin-1(x)1-x2

Q: ||| V3(x² + y²)dV, where V is bounded by y = 2x² + 2z² and y = 8.

A:

Q: y=Ax+Dx^B is the particular solution of the first-order homogeneous DEQ: (x-y) = 5xy'. Determine…

A: Given differential equation, 5xdydx=x-y,  x=3,y=6 dydx=x-y5x put, y=vx dydx=v+xdvdx now put values…

Q: The system x' = cos(t)x+ sin(t)y y' = cos(t)x - sin(t)y is linear.

A:

Q: xyz dV, where E is the rectangular box E = {(x, y, z) : –1 < x < 2,0 < y < 1, –3 < z< 0}.

A: ANSWER:

Q: 2. Find the most general antiderivative of f(x) = 3+22 %3D

A:

Q: y = x* + 1, y = 0, x = 1 around the ar axis.

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

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: 2. Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation to approximate…

A: Linear approximation of a function f(x) at x = a is, fx=fa+x-af'a

Q: Let ulx) be the solution of the IuP xy'-2y:x, yQ)=0 Evaluate y(32) %3D

A: In the question we have to find y(32).

Q: Y" - Y = { 2, %3D Ost Y(0) = Y'(0) = 0, %3D %3D t21

A:

Q: Display the values of the functions in Exercises 37–48 in two ways:(a) by sketching the surface z =…

A:

Q: ecos a tan(z+ x) 2x – y+ z V4x2 + y – z xyz T T T x + 2y + 3z 3x + 4y – 2z, x + y + z

A:

Q: y(y+2x - 2) dax – 2 (x +y) dy = 0

A: We have to solve the given non-exact and first-order linear differentiable equation…

Q: : // (x + y – 32) dV where E = {(x, y, z) | 0 < y < 1, 0 < x < y, 0 < z < r + y³} Evaluate - E

A: Triple integration

Q: How can I help you? use linear approximation to give an estimate for the value of g (0.97, 2.01,…

A: Given, g(x,y,z)=ze2x-y+cos(xz-3) To find Linear approximation to given estimated value…

Q: Find the general solution to dw ol Sa'(t) = x(t) – y(t) + 3e'; ly'(t) = y(t) – x(t) + 2e'; (8) (8)…

A:

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

A:

Q: xsin-1(x) is If x =0.1 and y = 0.11, then value of C in the antiderivative of F(x) = V1- x?

A:

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: dy f(x.y), y(x,)=y, by Euler's method is dx The third approximate solution of

A: Let us consider differential equation: dydx=f(x,y),   yx0=y0 Approximate solution of differential…

Q: The longest interval in which the I.V.P y" + (tanx)y-xy x, y(1) = 3, y'(1) = 0 surlay has a solution…

A: Given,  y''+tanx y'-xy=x It is of the form,  y''+p(x) y'+q(x) y=g(x)

Q: ntegrais. I, da, D= {(x.y) 0sxs20sys2% dA, D = x +2 [['e"d4, D={(x,y)| 0s ys 4,0sx<y}

A: Double integration