(6) Use the series representation of the function to approximate the integral with € < 10-4. Hint: Upon integrating the series use Alternating Series Remainder formula. (2) ²¹-2² dr. (h) (¹sin.x (cos(√T) dr dr (c)

Q: 1 where -1. n=0 n sum of ) 3" n=1 (Hint: This looks like a power series that has been evaluated at a…

A: Series summation

Q: +x (-1)" Given cos(x) = (-1)". n=0 (2n)! -x2n for all x E R, %3D 1. Express the integral cos x dx as…

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Q: 18. Find the Fourier sine series in 7/3, for 0<x<T|3, f(x)={ 0, for /3<x<2n/3, (-7/3, for 2r/3<x<n.…

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Q: series to approximate the definite integral I to within the indicated accuracy. [0.5 x³e-x² dx…

A: Series approximation

Q: p(0) p(1) p(2) 7. Let the linear transformation T : P2 → R³ be defined by T(p(x)) = and let %3D B =…

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Q: The polynomial given by (-x)* is the Taylor series for which function? k=0 (a) sin x (b) cos x 1 (c)…

A: Sum of infinite geometric series with first term a1  and commo ration r is given by a11-r. see below…

Q: 6. Find the sine series of Sx, f(x) 0 <x < #/2 - x, T/2 < x < T

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Q: -0.5 Approximate the integral 5x² e-x² dx with an error less than 0.001 using power series.…

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Q: For f(x) = 4 on (0,t), find the Fourier sine series of f(x). Make sure to write the series.

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Q: The function f(x) = Cosh(x) can be expressed by Taylor series as follow: Cosh (xi) 2!…

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Q: Let the improper integrals " sin(-)dx and sin?()dx (i) Write down the first 3 terms of Maclaurin…

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Q: Fin:d the Fot:ier sine seri:s in P T/3, for 0<x<T/3, f(x)= 0, for T/3<x<2r/3, -7/3, for 2n/3<x<r.…

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Q: (a) |r cos(a*)dz

A: As per our guidelines we are supposed to answer only first part. Kindly repost other parts in the…

Q: 1. Give a power series representation for the derivative of g(x) 2. Give a power series…

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Q: Evaluate the indefinite integral as an infinite series. ex- 1 dx 2x + C n = 1

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Q: 3. For z = e2x – 2x + 2y2 + 3 a. Find the critical point(s) b. Classify each point as a local…

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Q: Q5. Let the improper integrals, sin()dx and sin² ()dx (i) (ii) Write down the first 3 terms of…

A: Introduction: Sometimes the Maclaurin series is very efficient to integrate a function. The power…

Q: for this equation: y''-xy'+4y = 0, find the reccurance relation, use power series solutions x0 = 0…

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Q: The Fresnal integral is S(x) = o sin(÷ť²) dt. Find a power series representation for the Fresnel…

A: The Fresnal integral can be written as

Q: (ii) Find the area under the parabola y = f(x) = 9 – x² over the interval [0, 3] using summation of…

A: Given, the function is f(x)=9-x2 on the interval 0, 3 The area under this parabola over the interval…

Q: 6. Evaluate the indefinite integral as an infinite series. (b) / sin z (a) / r cos(r)dr

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