In Exercises 21–26, find the discriminant of the given function. 21. f(x, y) = e2* cos y 22. g(x, y) = e-&* sin(2y) %3D 24. g(s, t) = s²te¬st² 26. g(0, Ф) 23. f(s, t) = s³et/2 25. f(0, ф) — сos @ sin ф = cos e = cos e cos

Q: 4. Modify the Euler method to obtain the approximate values of y(3) and y'(3) y" – y' + y = t, 2<t<…

A: Given that    y"-y'+y=t                        1⇒y"=y'-y+t we will solve this problem through MATLAB…

Q: Suppose that Yt follows the stationary AR (1) model LaTeX:…

A: Given that Yt=2.5+0.7Yt-1+εt                         1  with Eεt=0 and Varεt=9 The standard ARt…

Q: 4.1 In aerodynamics and fluid mechanics, the functions u(x, y) and v(x, y) in f(2) where f(z) is…

A: We will find out the required values.

Q: EXAMPLE 2: dz 1 Given that z = x+y,where x = and y 2r. Find by: dt 1 a. Substituting x= and y = 2r'…

A: From the given problem:   z=x2+y2 ; x=1t2 ; y=2t3 a). Now, substitute x=1t2 ; y=2t3 in z=x2+y2 .…

Q: (a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

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Q: true false f(x) = R x −100 cos(t)dt and g(x) = R x π cos(t)dt are both antiderivatives of cos(x).

A: f(x) = R x −100 cos(t)dt and g(x) = R x π cos(t)dt are both anti derivatives of cos(x).

Q: b) Show that the “energy function" E(x, y) = 5 + is non-increasing along the solution, i.e., using…

A: (b) The objective is to show that the energy function  is non increasing along the solution, that…

Q: Exercise 3: Suppose that in an electric display sign there are three light bulbs in the first row…

A: As student want answer of only part 3,  So, I am providing the answer for that part only.

Q: Consider the following IVP: у" +у'%3D-сos x;B у(0) %3D а, у(0) -b Find the general solution. A y (x)…

A: Solution of the differential equation

Q: a1/ Find c; and ey so that ytx) = c; sin x +cz cos x will satisfy the given conditions. Determine…

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

Q: Problem 23

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Q: Let z(x, y) be the function implicitly defined as the solution to 2x + y + z + sin(xyz) = 4 + that…

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Q: Find the Tians Farm F(s) = "suy (27>1>0) (1 – s)(1 – e **) 3) f(1) = e',

A: Given problem:- Find laplace transformation of f(t) =et (0&lt;t&lt;2π)

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: Then, the only positive equilibrium point ỹ of Eq.(1.1) is given by Ei-1 di = (2.7) Li=1 provided…

A: We have a function H defined as Hu0, u1, …, u5=Au0+∑i=15αiui∑i=15βiui which implies that H is the…

Q: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)

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Q: 2(3) Calculate the following commutators: (a) [d/dx, x·d/dx] (b) [sin(x), cos(x)] (c) [x^2, Ĥ] ,…

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Q: (a) express dw/ dt as a function of t, both by using the Chain Rule and by expressing w in terms of…

A: Given, 1. w = x2 + y2 , x = cos t,  y = sin t;  t = π  2. w = x2 + y2 , x = cos t + sin t,  y = cost…

Q: 2. Show that e*, sin x, cos x are linearly independent using Wronskian Method.

A: As per the policy of bartleby the provisions is to solve only one question at a time  I am solving…

Q: Suppose that Yt follows the stationary AR (1) model Yt=2.5+0.7Yt−1+&varepsilon;t, where…

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Q: Solve the initinal - value pYo blem dy COsx - Sinz +y 0Lx<0.5 y()=0 Using (a) four th- order Runge -…

A: Given differential equation                                                   dydx=cosx-sinx+y,…

Q: A non-linear function is given by f(2) = a*-1 Where a is a constant. b) Define the perturbation…

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Q: (3) A study on optimizing revenue from a website considered dividing cus- tomers into two groups…

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Q: 2) Let 1 = f* cos y3 dydx. By reversing the order of integration of I, we get a. 1 = ²₂x cos y³ dx…

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Q: Express aw/ar and ôw/as as functions of r ands using chain rule w = = In(x² + y² + z²), x = res sinr…

A: Given problem is :

Q: 4y" + 24y' + 27y = 0 @y(Tt) = 1, y'(Tt) = 0* O y(x) = 6 [e^(3(t-T!)] cos(t/2) - e^(3(t-T1) sin(t/2)…

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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: az az and as Use the chain rule to find at (=) Z = tan V u = 8s + 5t, v = 5s – 8t az as az at

A: Topic:- derivatives

Q: 11. Show that the Beta function, defined by B(x,y) = (1-t"-1 dt , for x> 0, y > 0, satisfies the…

A: the given function is βx,y=∫01tx-11-ty-1dt for x&gt;0,y&gt;0 substitute t=1-s therefore, dt=-ds when…

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

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Q: 3) Consider a particle of mass m in a one-dimensional box of width L. Apply the variational…

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Q: 2.7 Given that the spacial components of motion, x = x(X, (), are: x₁ = X₁ + X₂ (e' - K), X₂X₁…

A: Solution : x1=X1+X2(et-K)      …(1) x2=X2+X1(e-t-K)   …(2) x3=X3    …(3) Solving above equations,…

Q: 1/2 Q2. a) Using Hilbert-Schmidt method, solve y(x) = cos 2x + 2 f,"´ K (x, t)y(t)dt, where Ssin x…

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Q: Suppose that w = x² + y² – z² | And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: Simplify w by substituting values of x , y and z and then solve the partial derivative.

Q: 4. Use the energy method to prove the uniqueness of the solution for the problem Utt = a²ug + h(x,t)…

A: Given problem is utt=α2uxx+hx,t      0&lt;x&lt;L, t&gt;0ux0,t=t2, uL,t=-t , t&gt;0ux,0=fx=x2-L2 ,…

Q: 7. Use Newtons method with the given X(0) to compute X(2) for each of the following nonlinear…

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Q: 4. (a) Prove that M(x, y) + N(x, y) = 0 can be made exact using an integrating factor that = f(x+y)…

A: To find-  Prove that Mx, y + Nx, ydydx = 0 can be made exact using an integrating factor that…

Q: Consider a regularizing term defined by where k!2* and the linear differential operator D is defined…

A: We are given the following regularizing term.                    ∫ℝN0DF(x)2 dx=∑k=0∞ak∫ℝN0DkF(x)2 dx…

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

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Q: Given the initial value problem y' = cos(xy) – x²e2* with y(1.5) = 0 i. Estimate the value of y(1.6)…

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Q: In Exercises 23–26, find ƒx , ƒy , and ƒz . 23. ƒ(x, y, z) = e^-(x2+y2+z2) 24. ƒ(x, y, z) = e^(-xyz)…

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Q: 1.Suppose that the joint p.d.f. of Y, and Y, is defined by: e-Y1/y2 · e-Y2 0 < y1 < 0, Y2 0 < y2 < ∞…

A: Given: The joint p.d.f of Y1 and Y2 is defined by:

Q: 4] I Let w = 5 cos(xy) – sin(xz); x = 1/t, y = t, z = dw using an appropriate form of the chain…

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Q: 4. Find the antiderivative of 1-t4 = CS the t that satisfies the given condition R(1) = 4

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

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Q: 3. Let V = eP cos(qr), with p = x In(xyz), q = z cos(Ty) and r = 2 tan-(y). %3D By using the chain…

A: Solve the given problem.

Q: If (х, у) %3D х" у"is an integratingfactor of the the DE. (1+ 3ху)dx + (ху-1 +x?)dy %3 0 Then, the…

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Q: 1 Find skewness and kurtosis for the RV X with PDF f(x) = 2T -∞ < x < x.

A: PDF of X,  fX(x) = 12πe-x22, -∞&lt;x&lt;∞ So, μ = E(X) = ∫-∞∞x f(x) dx=∫-∞∞x 12πe-x22 dx=0 [as…

Q: In Exercises 23–25, find ƒx , ƒy , and ƒz . 23. ƒ(x, y, z) = sec-1 (x + yz) 24. ƒ(x, y, z) = ln (x +…

A: We’ll answer the 23rd question since we answer only one question at a time. Please submit a new…