1) Using Taylor's formula show that e* = 1+ x +++…. x3 xn %3D 3! Zn=0 п!

Q: 13.Show that the third-order Adams-Moulton formula is yn+1=yn+h12(5fn+1+8fn−fn−1).

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Q: 23 4- [fe** dycdx ans :(e' - e' )(e² – e') 12

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Q: If x¨ + x˙ − 6x = e ^−t, with x (0) = x˙ (0) = 0, what is X (s)?

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Q: Example 7.13. Apply Bessel's formula to obtain y25 given y20 2854, y24 = 3162, y 28 = 3544, y 32 =…

A: Here we need to use bessel's formula to solve this problem.

Q: Question #: 5 An inventor claims that her new device will "drastically reduce" the oil consumption…

A: (5) Given Information: An inventor claims that her new device will drastically reduce the oil…

Q: (- 1)"x" .n (– 1)"x2n (2n)! (– 1)"x 2n+1 V3 = = n=0 (2n + 1)! n =0 n! n = 0 is asolution for D.E

A: Note that, ∑n=0∞(-1)nxnn!=e-x∑n=0∞(-1)nx2n(2n)!=Cosx∑n=0∞(-1)nx2n+1(2n+1)!=Sinx

Q: Find the first term of: E (-1)n+1 (z+1)" n=1 3D1 O (z+1)^2]/2 Z+1 -(z+1) no solution

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Q: 7) Use Theorem 7.1.1 (Table) to find L{f(1}} for the following: S)-(e*-e*)}° a.

A: The given function is f(t)=(e-3t-e5t)2. Expand the function implies, f(t)=e-6t+e10t-2e2t The Laplace…

Q: 2) S . dr V-1

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Q: 4x obtain the section of the equation Ex xl with the condition u oon X4

A: Let us consider the given PDE is P(x,y,u)ux+Q(x,y,u)uy=R(x,y,u) The equation is solved as Determine…

Q: 7. Solve the initial value problem described by PDE:u„ – c²u = e* with the given data u (x,0) = 5,…

A: The guven Initial value problem has been solved below.

Q: 5. Using the Bernoulli method, solve the following DE. (a) y+ay ay %3D

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Q: Find solution of the problem in the form of the normal mode u * eo-xlc) and discuss the result a²u…

A: Given that : u=eiw(t-xc) Simplify it, we get : u=eiwt.e-iwxc. We know that : eiθ=cosθ+i.sinθ .…

Q: A radioactive sample decays according to the law - -hy where k>0 Suppose c represents the size of…

A: From the given differential equation:   dydt=-ky   So, dy=-kydt...Integrating on both…

Q: If z + In(e3* - e + e²) = 0 dz find at the point (0, 0) -3 -2 3. 2.

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Q: 2. Solve f e** using Simpson's 1/3 Rule with n = 8.

A: The Simpson's 13rule is given below by,  ∫abfxdx=h3fx0+4∑i=1, i is oddn-1fxi+2∑i=2, i is…

Q: Question (1)  Prove , ez1/ez2  = ez1-z2

A: The given equation is: ez1ez2=ez1-z2

Q: 4. Let X-f(x;8) where f(x;0) = 0 (1-0)-10.1)(x), 8 € [0,1/2]. %3D a. Find the MME and MLE of e. b.…

A: Given that  X~ f(x,θ) where the probability mass function of X   X follows the Bernoulli…

Q: 1) Evalúe a) csch (In 3) b) cosh (0)

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Q: 7:31 MAC2311C-FINAL-A PDF - 234 KB 10 Problem 10. The value of the integral nz dx equals: (A) In 2…

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Q: Apply the secant method to solve ƒ(x) = e*² In x² – x = 0. Discuss the procedure for dealing with…

A: We are given the following function. f(x)=ex2lnx2-x=0 We have to solve by the secant method. Note…

Q: - S e-ttat1-1 dt a # 1 a '0

A: We use the definition of the Gamma Function to solve the given question.

Q: 2. Define Ej where the reactor rise time of the first batch is less than 55 min. and E2 where the…

A: Given: E1=The reactor rise time of the first batch (t<55)E2=The reactor rise time of the second…

Q: 2. J고dr (e* -1) (e +1)

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Q: ind the solution to an initial value problem (IVP) x" +x = with initial conditions x(0) = x' (0) =…

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Q: Show that r n2n-1 r=0

A: Want to  prove:    ∑r=0n rnr=n2n-1

Q: 1. Expand x³y²(x + y)12. E15.(15) xn+3y15-n ,15-п а. n 12 b. Eo () xn+3y14–n ELo (5) xn+3y14-n С.…

A: From the given information. The given expression is .

Q: 4 Σ E Vn +1 n=-1

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Q: 7. Find the explicit particular solution to the initial value problem. Hint: Linear DE. у 3 cos (x)…

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Q: 2) y-Sy=-5xy* Type:? find general solution. 3

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Q: 25x g(x) = In(3 + V7 ) dt Find g'(8) (A) In(43) – In(3 + V4 ) (B) - In(43) – In(3 + V4) 2Vs (C)…

A: We have to find the integral

Q: Solve the Cauchy-Euler initial value problem (2 x² y" – x y' + y = x, x>0, y(1) = 0, y'(1) = 0. Find…

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Q: 2. Prove that the equation e + x° 0 has exactly one solution.

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Q: 4. In one model of the changing population P(t) of a community, it is assumed -, where and are the…

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Q: 2.4.10 Show that det(e4) = etr(A) for all A E Mn(C). D %3D

A: The given problem is to show the given identity. To show: det(eA)=etr(A) for all A belongs to Mn(C).

Q: 6. 81n V81 - 81 – x²dx 4 A. Show that B. Use (A) to evaluate In 4 (e2x – e*) /81 – (e* – 1)* dx. - -

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Q: centered at z = -1. (-1)" (n + 1)(x + 1)" n+1 E"(z + 1)" Σ n! O m-0 El-1)~ (n + 1), (x+1)" n!

A: 1. The function given is fx=1x2. At x=-1, f-1=1. Finding the derivative of the function at x=-1. The…

Q: L %3D e2t e-3s-6 (s+2)? O e6-3s ( 1 3 + S+2 (s+2)2 O e-3s (s+2)2 1 3 s+2 O e2-3* ( +) 1 (s+2)2 s+2 O…

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Q: (3) In one model of the changing population P(t) of a community it is assumed that dP dB dD dt dt dt…

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Q: d If g (x) = ª[e' - In(21 + 1)]dt, find g(x) . dx A e-In(2x+1) 4 (В et + (2x + 1)² 2 (C) (2x + 1)² 4…

A: Topic:- application of integration

Q: Ex: Find the solution of The e ditt evential equation xy? with yCi) =1 2xy 2 dy

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Q: 47. Let the assumed particular solution for the given DE be yp = (Ar + Bx² + Cx)e + E. What is the…

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Q: Apply Heaviside's expansion formula to 3s +1 (s− 1)(s²+1)

A: Here we have to find the Laplace inverse of 3s+1(s-1)(s2+1) i.e. L-1[3s+1(s-1)(s2+1)] by applying…

Q: If we use a linear approximation of e- at a = 0 to approximate e-1/3, then we obtain: А. 4/3. В. 2/3…

A: The solution is given below

Q: Q2) let A = [ 1 find e4t using Gauss-Jordan method.

A: First we will find the eigenvalues and corresponding even vectors of the matrix by Gauss-jordan…

Q: If z3 + In(e 2 -2 e+e) = 0 az find at the point (0,0) O -3 0 3 О-2 O 2

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Q: 17. Find the values of p for which the integral 3-2, dx converges. 3-2p Орe(-1,1) Op > 1 Op 1 Ops1

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Q: Given that n2 1 and xn =V 4n² + 3n – 2n Will {Xn}, be divergent or convergent? n=1 Will E-1 Xn be…

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