Apply the open Newton-Cotes formula with 3.5 xe*dx n=1 to approximate 0.5

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A: We have to evaluate the integral ∫e−1e2logexxdx. Substitute logex=u ⇒1xdx=du And limit of u is u=-1…

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Q: Find n so that 27 en+1 – 1 < 0.05? 2 (n + 1)(n + 1)! Use the information above to calculate eet dx…

A: For (b), We need to find n so that 272en+1-1n+1 (n+1)!&lt;0.05. Notice that solving this…

Q: a) Use Newton's Method to find an approximation of: accurate to within 10-3 V5+1

A: First we will obtain the equation which will have the value    as its root. then we will obtain the…

Q: Evaluate the following definite integral: dx = 12

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Q: e ax dx

A: 1. Let In=∫xneaxdx. Use the integration by parts formula ∫udv=uv-∫vdudxdx to evaluate the integral…

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A: Zero of a function is the value in its domain for which the function takes the value of 0. Newton's…

Q: Evaluate dx by using Simpson's 1/3, taking n= 4, correct to four decimal places log,(e)

A: Consider the integral  ∫45.21log5exdx

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A: We need to find ∫cosxsinxesinxdx by using substitution followed by integration by parts. So,

Q: 4. Find the V2 accurate to 6 decimal places using Newton's Method.

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Q: Use the error bound to find the smallest value of N for which Error(SN) < 10-º. 6er dx (Give your…

A: Given  ∫016ex2dx

Q: Find Newton-Raphson formula to obtain th

A: Given,           57

Q: Use the data below to estimate the value of f(6) to two (2) decimal digits using Backward…

A: Given the table for x and y=f(x).     x     1     3     5     7     9    11   f(x)   0.01…

Q: Find the value of the positive integer A so that: In A 1 sinh x dx 4 Jo

A: ∫0lnA sinhx=14 coshx0lnA=14 coshlnA-coshln1=14 coshlnA-cosh0=14 coshlnA-1=14 coshlnA=14+1…

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Q: Use Newton's method and find an approximation for the root of the following function accurate to…

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Q: Find cosh a In(sinh r)dr.

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Q: Evaluate the following integral. 12 S 0 4 log 13 (x + X + 1 1) -dx

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Q: 23.) Use Newton's Method to approximate V7 correct to six decimal places.

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Q: Use Newton's Method to approximate v13 correct to six decimal places.

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Q: Use Newton’s method to find approximate answers to the following question.

A: To find f'(x), differentiate the function f(x) with respect to x. fx=exxf'x=ex-1x2+exx=ex1x-1x2

Q: Evaluate v12 to four decimal places by Newton's iterative m

A: let x=12 x2=12 therefore f(x)=x2-12 differentiating f'(x)=2x f(3)=9-12=-3 also  f(4)=16-12=4 since…

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Q: Q1. What does the Newton's method produce to the actual root by repeating the approximation?

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Q: The approximation of 3x e sin(2x) dx by Simpson's Rule is 2.584696

A: We have, ∫0π4e3xsin2xdx Let Number of subintervals be 30.…

Q: Find cosh r In(sinh a)dr.

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Q: 2. Approximate the sol of x = sinx upto 4 decimal places by using Newtons method. Eind th ainta find

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Q: For the function f(x) = cos(x), write Newton's formula f(xn) F(xn) for solving as xn+1 = = Xn f(x)…

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Q: 3. Find a positive root of cosx - xex = 0 upto four decimal places, using Newton-Raphson mehtod. %3D

A: I am attaching image so that you understand each and every step.

Q: The bacteria in a certain culture increase according to dN/dt = 0.25N. If originally N = 200, find N…

A: Integrate the equation.

Q: 2) Solve the following integrol with details. -21 r3 cos? Oredr sinQdo =x 2 32TT a x=?

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Q: Solve the folkowing di fferential equotions 1. xdy dx + dy x'

A: Firstly , we can solve for dydx. After that we can see that the equation is an homogeneous…

Q: Solve the following integral xe* dx 1

A: Calculate the integral         ∫12xex3 dx

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Q: . Use the Newton's method to find a solution for f (x) = x'-e* on [0.5, 1] within ɛ = 10*. Use po =1…

A: In numerical methods there are number of methods for calculating roots of a function. Some them are…

Q: Does the following integral converge or diverge? Justify your answer. 112 dx /x°+13 8

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Q: (c) Prove, using the definitions of sinh and cosh in terms of the exponential function, that…

A: The solution is given as

Q: S 3* e*dx

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Q: Evaluate 1- x? dx 0. by Simpson's rale with n=5

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Q: L(3x+e")dx Jo

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Q: Use Newton's method with initial approximation x, = 1 to find x,, the second approximation to the…

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Q: Calculate SN given by Simpson's Rule for the value of N = 6. 1 cos (4x?) dx (Round your answer to…

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Q: a) Use Newton's Method to find an approximation of V5-1 accurate to within 10-3

A: Note "As per our company guidelines we are supposed to answer ?️only first question. Kindly repost…

Q: Calculate SN given by Simpson's Rule for the value of N = 6. I cos(2x² ) dx (Round your answer to…

A: given the expression is , SN given by simpson's rule for the value of N=6 ∫01cos(2x2)dx

Q: is equal to A Inr+ B ln s where A = and where B =

A: Given expression :

Q: Comment on using the Newton method to compute the root of the function f(x) = x¹/3, i.e., if your…

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