4. Find the divergence of U = e*Yax + sin(xy) ay + cos²(xz) a,. А. уе*У + х сos(ху) + 2х сos(xz) В. хехУ + у сos(ху) + 2х сos(xz) C. ye*y + x cos(xy) + 2x cos(xz) sin(xz) D. xe*y + y cos(xy) + 2x cos(xz) sin(xz)

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A:

Q: -1 < x <0 The Fourier integral of f(x) = 1, 0<x<1 0, otherwise 00 (1 – cos(w)) sin(wx) dw lw 1. 00…

A: Given that fx=-1-1&lt;x&lt;010&lt;x&lt;10otherwise The Fourier integral of f(x) defined on -∞,∞ is…

Q: e Divergence Theorem to evalu (4x + 10y + z²) dS Js

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Q: 1. Prove that for all x, y ER, max (x, y) = x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y}=-

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Q: Use the Laplace transform to solve the initial-value problem: [y'+4y=3 cos(3x), y(0) =5] --꽃 12 137…

A: By using the standard formulas of Laplace transform, the given initial value problem has solved in…

Q: 28 + 4 What is the value of the inverse Laplace transform given by L { g2 + 2s + 3 O a. 1 je+(4…

A: The given expression under the inverse Laplace can be written in the partial fractions as below:…

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A: Option (a) is true.

Q: 5. Use Laplace transforms to solve the initial value problem y" + 3y - 10y = 13(1-cos(t)), y(0) = 1,…

A:

Q: A damping system with a negligibly small spring constant is modelled by x"+bx'=aebt with x(0)=0 and…

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Q: Suppose an undamped forced spring mass system is driven by the equation + 9x = f(t), dt where the…

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Q: Use the Laplace transform to solve the given initial-value problem. y(t) = y" - y'= et cos(t),…

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Q: Find fy if f(x, y) = sin 5x cos 5y O fy = 5sin 5x sin 5y fx = cos 5x cos 5y O fx = 5cos 5y cos 5x fx…

A:

Q: Find the divergence of = ea + sin(xy) a + cos² (xz) a X O yey+x cos(xy) - 2x cos(xz) sin(xz) ọ xe…

A: U→=exyax+sin(xy)ay+cos2(xz)az

Q: Find the particular solution of y' - 2y = e3x if y(0) = -5 using Laplace Transform. %3D %3D

A: The given initial value problem is                                               y'-2y=e3x , y(0)=-5…

Q: the Following is divergent

A:

Q: dw Use the Chain Rule to find dt w = 7x°y°z,x = 2t, y = cos(4t), z = tsint %3D 7xy°(12yz -…

A: see 2nd and 3rd step.aa

Q: 2. Show that if zo is an isolated singularity of f(z) that is not remov- able, then zo is an…

A: We have to show if z0 is an isolated singularity of f(z) that is not removable, then z0 is an…

Q: Find the differential dy: y = In(sec² ( 3ª²–20+5 312-2x+5 O (E) None of the choices dy = 2 (x – 1)…

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Q: *) Use the Wronskian to determine whether the functions y₁ = sin(3x) and y₂ = cos(4x) cos(4x) are…

A:

Q: X1, ., Xn are idd. find the MLE and cramer rao lower bound for unbiased estimator for theta. f (x |…

A: Given  fxθ=θ              when x=-11-θ2θx     for x=0, 1, 2, ....

Q: (a) x = t* - t + 1, y = t2 Select--- v (b) x = 2 - 2t, y = VE --Select--- v (c) x = sin(2t), y =…

A: Match the graph with their parametric equations.

Q: Find the divergence of U = r cos 0 a, - sin 0 ag + 2r² sin 0 2 sin 0 3 sin 0 - r2 2 cos 0 3 cos 0 r2…

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Q: Sow that 2 x² + y² + z² - c²t² is Lorentz invariant.

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Q: 2. Show that the Euler-Cauchy Equation Iy" + axy + by = 0, 1+0 can be transformed into the constant…

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Q: Suppose w = In(8x² + 2y² + 3z²), ¤= 9 cos(t) , y = 9 sin(t) , and z = 8Vt. Compute dw/dt in two…

A: The partial derivative of a multivariable function with respect to any of the variables can be…

Q: Q2) Solve the initiai value problem by Laplace transform. y" +4y=cos 2t y(0) = 1 , y'(0) = 1

A:

Q: Now, 2 x (+) dt 2 50, d2x(+) dt 2 -1 d2x(1) dt 2 is +2 J2x(+) ct 2 + 1 +2 = -15(++ 2) + 25 (1-0) +…

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Q: t, 01 1 a.) f(t) [m (sh w + (cos w - 1)] cos wt + [[ -[sin sin OLL - cos w + sh w]]sin wet dw - 1…

A: Given the function is ft=t0&lt;t&lt;10t&lt;0, t&gt;1

Q: 3s+2 Compute the inverse Laplace of Y (8) = 32+25 3 cos 5x + sin 5x 2 cos 5x + sin 5x cos 5x + sin…

A:

Q: If Σ An diverges then > can diverges O only if c>0 O only if c< 0 O only if c+0 O for any real value…

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Q: 2 2 If z = f(x, y), where x = s² - t² and y = t² s² and z is differentiable, then - Select one: True…

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Q: 2. Find the linearization L(x, y, z) of f(x, y, z) = x² + xy + yz + 22 at the point (0, 1, 2).…

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Q: (a) express ux, u y, and uz as func-tions of x, y, and z both by using the Chain Rule and by…

A:

Q: 22) Solve the initiai value problem by Laplace transform. y"+4y cos 2t y(0) =1, y'(0) = 1

A: In this question, we are asked to solve the Initial value problem by Laplace transform Equation :…

Q: If f(z,y, z) = I COs(2y – 2). compute and af and Te Əz =I Cos(2y -2). compute O = cos(2y2) I sin(2y…

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Q: 1 - Show that u(X, y) - e^Cosy is harmonic function = e and Find tne Conjugate harmonic v(X,y) and…

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Q: Assume that after w months, butterflies’ populace in 1000 is calculated as: f(w)=12w+cos⁡(16w)+n×100…

A: Given: Butterflies’ populace after w months is given by f(w)=12w+cos⁡(16w)+n×100 in 1000 where n=824

Q: Əz 1 Q3.If Z= f(x,y)=4e* ln(y), and x = ln (u cosv), yusin v, use chain rule to find : 201 ди and az

A:

Q: 5. Use Laplace transform technique to solve v"-y'-6y = 0, Given v(0) = 1 and y'(0) = -1

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A:

Q: show that f(z)=(z-1) cos(1/z+2) has an essential singularity at z=-2

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Q: Use the Laplace transform to solve the given initial value problem. y" + 4y' + 13y = e=2# sin3t,…

A: Solution

Q: a) Sojlve the initial vajlue problem using Laplace transform UTM y + 2y = 26 sin 3t, y(0) = 3. UTM…

A:

Q: Let f:R^2 --> R^3 be given by f(x1,x2)=(e^(x1+x2^2, x2+cos(x1,x2), x1^2+x2^2+2) Compute the…

A: Using jacobian matrix,

Q: If (2, 1) is a critical point of f and fzz(2,1)ƒyy(2, 1) < [ƒzy(2, 1)]², then ƒ has a saddle point…

A: Here, the given statement is: If (2,1) is a critical point of f and fxx(2,1)fyy(2,1)&lt;fxy(2,1)2…

Q: Which of the following graphs is the slope field for dx 12 -3-211. s 2 13 US 111-2-/35 1112 111²-111…

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Q: Please solve this Differential Equation question. Thank you!

A:

Q: 4)Use Laplace transform to solve y +2y +2y=e", y(0) = 2, y'(0) = -1

A: Given y"+2y'+2y=e-t , y0=2 , y'0=-1 Ly"=s2Ly-sy0-y'0 Ly'=s Ly-y0 Le-t=1s+1 Now…

Q: Suppose z = 2xy where x = t^2 + 1 and y = 3 - t. Use the chain rule to determine which of the…

A: In the given question the functions are given as z=2xy , x=t2+1 , y=3-t . The objective is to find…

Q: 1. Find the linearization of r – z at a = 2.

A: Find the linearization of x3-x at a=2.

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.