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

Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler or Runge-Kutta method, what is…

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Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

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Q: Given y In(z+1) dy what is ? dy dz z+(x+1) In(z+1) 1²(x+1) (z+1) In(z+1)–x 1²(r+1) dy z-(x+1)…

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Q: (x – cos y)dx – sin ydy = 0 Of (x, y) = -xe-# +e-* cos y + k (y) ;f (r, y) = -e- sin y dy +k (y) Of…

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Q: Let f(x, y,z) = x² sin y + y e², where x =t + 3,y = net-1 and z = In 2t. dL at t = 1 is: 1-2n O -12n…

A: Given, fx,y,z=x2siny+yez, where x=t+3,y=πet-1 and z=ln 2t.   The objective is to determine dfdt at…

Q: Evaluate |[[p(4z + 3y² + 2x)dV = {(x, y, z) | 0<x < 2,0 sys 2, 0 s z < 1} .

A: We have to evaluate the triple integral given below: ∭B4z3+3y2+2xdV  Here, the region B in three…

Q: Let f(r, y, z) = ln(x² + z) + y²e#² – cos(2yz). Find fzyr- %3|

A: Consider,                                                                 f(x, y, z) = ln(x² + z) +…

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: Find the valve of k so that (2y sın x cos x -y + 2 y e** ) dx - (x - sın' x + kxye*) dy 0 becomes…

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Q: 3. Find the total differential of z = f(x, y) if z2 - y = (1– 2x)z.

A: Total differential of a function z=fx,y is dz=∂z∂xdx+∂z∂ydy

Q: riable t. If 2sin (x)+4cos(y)=3a dy and dt 3, what is the val

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Q: 10. Find the linearization, L(x,y,z) of the function f (x, y, z) = e* + cos(y + z) at Po (0,",").

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Q: Given the function f(x,y) cos 2xーx3eY +āyン COS find te second partial olerivative fxy.

A: Let f(x,y) is the given function.Then  fx is the derivative of f with respect to x taking y as a…

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

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Q: (y In a In y) dr + dy = 0 O In In y| + x Inx +x = C O In y = Ce" r* O y = eCe*z* O y = eCe*z ts)

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Q: Given (1+ 3x sin y) dx – x² cos y dy = 0 with y(1) = 0. Using Euler or Runge – Kutta method, what is…

A: Given 1+3xsin ydx-x2cos y dy=0....(1) with y1=0 We will find the value of fx, y to approximate y

Q: z = In (VT" + y") If With n e N, n > 2, Then the result of 2 (dz dy dz n Corresponds to: "-1 + y"-1…

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Q: 22. u- Vr? + s, r- y + x cos 1, s -x+ y sin t; ди ди ди when x= 1, y = 2, 1 = 0 ar ay at

A: Given: u=r2+s2  r=y+x cos t and  s=x+y sin t By using Chain Rule we have to find: ∂u∂x, ∂u∂y ,and…

Q: 2. Let f(2) = 2°e* z + 0. What type of singularity does f(z) have at z 0? (Justify.) What is the…

A: the point z=0  essential singularity.

Q: Let f(x, y, z) = ln(x² + z) + y²e#z – cos(2yz). Find fzya.

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Q: f(x) = In(2 + cos x). -2.125, xk+1 = Ik +0.5, yk = f (xk), k E N To = %3D %3D = 0r

A: The function is fx=ln2+cosx Conditions: x0=-2.125, xk+1=xk+0.5, yk=fxk, k∈ℕ xk+1=xk+0.5…

Q: y = In z I at x = 1: Oy=-x+1 Oy=-x-1 Oy=x-1 Oy=x+1

A: As per the company's guidelines, we are supposed to solve the first question for you, kindly repost…

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: 2. In each exercise, obtain the particular of solution. a. xy dx + 2(x² + 2y²) dy = 0; when x = 0, y…

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Q: a When reduced to a linear DE of order one in z, the Bernoulli's equation dx becomes dz A + z( − 1)…

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Q: A) If w = 2 y et* – In z where x = In(t² + 1), | dw y = tan-1 3t and z= e3t. Find by Chain Rule dt

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Q: 22. u = Vr² + s², r = y + x cos t, s=x + y sin t; ди ди ди əx’dy when x = 1, y = 2, t = 0 dt

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Q: Let f(x, y,z) = x² sin y + y e², where x = t + 3,y = net-1 and z = ln 2t. %3D df at t = 1 is: dt…

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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: : 0s 0s n, Os zs 1, 6Vzs rs 6}. Let E= Compute y?e(x2+y?)³ dv•

A: Given that, Let E=r,θ,z : 0≤θ≤π, 0≤z≤1, 6z≤r≤6 compute ∬∫Ey2ex2+y22dV

Q: 8. Let f(x, y) = cos(y – x) and r(t) = (e', e2t). Find if (r(t)) at t = ln(3).

A: The solution is given as

Q: y 1) x(In x – In y)dy – ydx = 0 Ans: = c (Xie, 2010) %3D 1+In y-In x

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Q: 1. Find the total differential dw. x + y +z 3. w = xyz

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Q: ution of yl = x+xy2 W

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Q: At what points (x, y) in the plane are the functions in Exercises 31–34 continuous?

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

Q: 2. Give an interval of the form (a, b) around r 1 such that the IVP has a unique solution. dy = sin…

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Q: 12. Express ſ S S Vxyz(1 – x – y– z) dx dy dz in terms of u, v,w given that x + y +z = u, y+z = uv…

A: Express the Mathematical expression for Jacobian transformation of x=x(u,v,w),y=y(u,v,w) and…

Q: 1. Given dy dy +2- + 5y = e¯* dr² and y(0) = 0 and = 0 find the value of y(0.1) and y'(0.1) using…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 1. Let z = f(x, y), find for: and dy - - (a) e"y + z ln y = 0 (b) yz – sin z = xy

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Q: 4. Evaluate ryz dV, S is the solid in the first octant S bounded by the cylinders x² + y² = 4 and x²…

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Q: A:= {(x, y) € R² :1< log(x) < 2}. = {(x, y, z) E R³: sin(xy² + «/2) · cos(z) = 1} . (a) Decide…

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Q: a Z2=2+4i - [ (3 Im (2) + 2 Re (2)] dz Let e = 21=0 where C the parabola y = x² defined from z1 to…

A: Solution: (a) Let us consider C be a parabola y=x2 defined from z1=0 to z2=2+4i. Therefore, C can be…

Q: Solve the problem with Neumann boundary conditions, 0, x, t>0 u, – Ugg = u(x, 0) = f(x) u;(0, t) = 0…

A: we have ut=uxx ux,0=fxux0,t=0 Fcut=Fcuxxdu¯dt=-su⇒u=Cse-s2tNow, ux,0=fx⇒us,0=f^cs=Cs⇒u=f^cse-s2t Put…

Q: flx, v) = { xe-x(1 + y) x20 and y 2 0 otherwise rmine E(XY). ulate Cov(X, Y) and p. X, Y) =

A: Given Two components of a minicomputer have the following joint pdf for their useful lifetimes X and…

Q: Suppose x, y, and z are positive functions of t. If z x + y?, dx/dt 1, and dy/dt 2, find dz/dt when…

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Q: 1. Evaluate a dV where E = {(x, y, 2) E R³ | 0 < z < x + y,0<x < y?,0 < y< 1}.

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler or Runge - Kutta method, what is…

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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: b) Evaluate the triple integral S dx dy dz re3 1 xyz

A: