Q4 Legendra polmomial Pe (X) =2 + (3x+1) than Prove that (2u+1) Puck) =Pmnil (X) -P(X) n-1

Q: Evaluate I = √x+e²×¯¹dx 2x-1 a) By using Trapezoidal rule with 12 segments b) By using Simpson's one…

A: The given integral is I=∫17x+e2x-1dx. To Evaluate: (a) Using Trapezoidal Rule with 12 segments. (b)…

Q: If you apply two steps of the Secant Method to x3 = 2x + 2 initial guesses x0 = 1 and x1 = 2, Then…

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Q: (n² – 3n – 21) ÷ (n –7) -

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Q: S xdx can be solved by either algebraic subsitution or integrataion by parts. Vx- 1 A True B False

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Q: Estimate the value of gqΣn=2 to ∞ (1/(n2 + 4)) to within 0.1 of itsexact value

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Q: 1. Using the first prine =) , show that (1 – x*) + 4nxy = 0. %3D 2. If y = 1+x2, + qx2+rx +s passes…

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

Q: Consider the following problem; max(x? + 2y) s. to 5- x2-y² >0 and y 2 0

A: Consider the given function. fx,y=x2+2y and x2+y2≤5. Use the Lagrange Multipliers to calculate the…

Q: 2 (ii) using Convolution theorem. (s+2)(s²+9)

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Q: a. My =n xyy

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Q: Show that kT| e-t²/kTdt = (kT)3/2 " 0. 2

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Q: 5.2 Q3: By using Trapezoidal rule find I | In xdx , where n=6.

A: The objective is to find the integration of the given function in the interval [4,5.2] by using…

Q: Q4: Use the Gauss-Seidel iterative technique to find approximate solutions to 10x -x +2x3 -x +11x2-…

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Q: 4. y= 5e, y-s+ax-3x between x-0 and x=1 about y= -3

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Q: 5- Find L-1 5² (s²+4)² by using Convolution theorem.

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Q: determine the second approximation Xz if Ne wtons Method was use to defermine the root o f the…

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Q: Find the general solution of y' + ny = emx for all m, n. Note: The case m = −n must be treated…

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Q: 2.5 Solve for z if cosh z = V3i.

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Q: O we N. P.M. to estimate the root of -X for on initial guess of Xo

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Q: Q3. Verify that y² = x² – 3 is the particular solution to the following ivp: y' = ; y(2) = -1. %3D

A: To check whether a solution is particular solution to ivp , it must satisfy the differential…

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: Find extreme value(s) of z = 2x¡ + x,xX2 + 4x3 + x,x2 + x} + 2

A: Consider the provided question, According to you we need to solve only part (d). (d)

Q: 5.) Consider the fonction fas= x'+ex²+lx +6 Evaluat e Ho) - fc-4) 6 - (-4) fCx) di ffer entiable on…

A: Given:       f(x)=x3+6x2+11x+6

Q: xdx S- can be solved by either algebraic subsitution or integrataion by parts. x-1 А) True B) False

A: We know that algebraic substitution is method in this replace the veriable of integration by a…

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: Find the general Selution yer r the equatiJen S/0x)-14 ()+ 0 By(x) = =D0 dlax

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Q: 4 Find the general Solution of the following PDES • з Их + 2 Иу -Х u(x,c) =4е 2 (зу-2х)12 ans3- и(x,…

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Q: 6. Find the smallest constantr so that o(x) == x" is a solution to 3z'y" +11lry -3y= 0, for z >0 -3…

A: 6.ϕr=xr is a solution to 3x2y''+11xy'-3y=0, for x>0

Q: e. y= (x² + 4)/x in the interval 1<x<4. 8+ 4ln4 - % s.u ans.

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Q: Solve for X(n) using any 2 out of 3 methods of the given X(z). 1 X(z) = (1– z--)(1– z-2)

A: Given z‐transform can be written as Xz=z3z-1z2-1=z3z+1z-12

Q: convcrges for all r. n! n=1 Σ 24. Show that

A: To show the series∑n=1∞rnn! is convergent for all r; ratio test can be used. Ratio test rules that…

Q: By= In(Cx-2)

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Q: the next iterative value of the of x² - 4 = O using secant method, if the initial guess is 3 and 4

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Q: Q: Examine y (o.4), Using Runge - Kutta Order 4 method if X = 4n + 2

A: Given y′=4x2+2y,      y(0)=1,   h=0.1,   we have to find y(0.4).Forth order R-K…

Q: Use Horner's method to evaluat P(x) = 2x – 3z? +3x -4 at xo = 2

A: Horner's method (also known as Nested scheme) uses synthetic division to evaluate the function:…

Q: it as a Bernoulm cquaion in the uependeht varlavic A. 0. 2x'y = y(y? + 3x). Solve by two methods.…

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Q: 8) (a). (8pts) Find a general solution to y" – 6y' + 9y = t-³e³3t by using variation of parameter…

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Q: Thene m for Voritly functiom Mean Valne fex) 2. 3X -4 +S the

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Q: 12. Find the general solution using Reduction of Order: a) y" = 31n x

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Q: Consider the initial value problem V5y – 7 6t2 - y(to) = y0 Existence and uniqueness is guaranteed…

A: Given that y'=5y-736t2-4,   y(t0)=y0

Q: 4. If the secant method is used on f(x) = x^5 +x^3 +3 and if x_(n-2) = 0 and x_(n-1) = 1, what is…

A: The given function is,

Q: 7. Consider the IVP y'=(2x-4)e" with y(5)=0. Verify that y = In(x² – 4x -4) is the solution to the…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 2s + 5 cosh t L- s2 + 6s + 34 et 5s L-1 (s – 2)² 3t -

A: Laplace transform of the function

Q: Also p; 2 0 for all j = {1, ., k} and E-1P; = 1. What is the value of E(X) and V(X)?

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Q: Consider the following problem; max(x? + 2y) s. to 5-x² - y >0 and y >0

A: Extreme Value Theorem- If f(x,y) is continuous in some closed and bounded set D in ℝ2, then there is…

Q: Q3M) Given the IVP x²y' +2xy = cosh x, y(1)=0: a) Determine the explicit solution by providing and…

A: Since we only answer one(first) of the multiple question from the given multiple no. of question.…

Q: is the minimnurm step of the horno gone ous n What X+ xt 2-X ifferential equatian with its solution…

A: The objective is to find y=x2e-x+x3+x2what is the minimum step of the homogenous differential…

Q: Is a solution of the diffrntish epuation 1 yy'= -X+ with y E € ]_9,GE with x € C-G,G] 2. 3)yy:…

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Q: y = c,e2x + c2xe2x + C3x²e2x

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Q: 5: A. Using convolution to find L¹ [(5+2)(s+4)

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Q: Ivy is not sure whether a particular c the coin is not fair if she observes 4 4.24 and alternative…

A: Ans: