2. If we only add four terms of the series 2-V, estimate how far off (at most) we could be from the actual sum.Hint: u substitution with u = n can turn this into integration by parts. Also, the derivative of 2" is In(2)2" and the antiderivative is In(2).

Q: 0.2 1 dx to five decimal places using the power series from 1+x b) Estimate

A: Note that the power series of 11+x is: 11+x=1-x+x2-x3+x4-x5+... Replace x by x3 we have:…

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Q: (1 – x + x²)y" – (1 – 4x)y' + 2y = 0.

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Q: Find the first four nonzero terms in a power series expansion about x = 0 for the solution to the…

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Q: Evaluate the indefinite integral as an infinite series. ex 1 3 2x xp + C n = 1

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Q: Evaluate the indefinite integral as an infinite series. et 2x – 1 dx 3 )+c n = 1 8.

A: It is given that, 3∫ex-12xdxwe have to evaluate the indefinite integral as an infinite series.

Q: If the kth partial sum, SŁ of the telescoping series E [sin(v4n) – sin(/4(n+ 1))] n=1 is given by…

A: We will use formula for kth partial sum and compare the result with given Sk

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Q: Note that you only have one chance. The power series of sin(x) at x= is given by k=0 (2k+1)! k=0…

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Q: The series E-1 and improper integral S dx converges and diverges at the same time.

A: the statement is true

Q: In(x84 dx The integral converges to 0 converges to -336 goes to co дoes to -oo converges to 336

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A: We use the power series method to find the solution of the given differential equation.

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A: Explanation of the answer is as follows

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Q: Let y(x) be the solution of the initial value problem dy 30°y, y(2) = 3x?y, = 3. dx Use Taylor…

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Q: 0.25 S In(1+ VT)dx

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Q: compute the values up to four decimal places of the following using maclaurin's series: Sinh^2 (0.5)

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Q: apply the successive approximation In Problem. formula to compute yn(x) for n < 4. Then write the…

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Q: Find the first four nonzero terms of the Taylor series about 0 for the function f(x) = 1+x cos(6x).…

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Q: Q1: Use series to approximate the value of integral: ーX-1 0.2 e 1-

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Q: 6. The improper integral 1 dx converges to х -5 попe 2 1 4

A: We have to find

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Q: Compute the value of the following improper integral. If it converges, enter its value. Enter…

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Q: #2. Find a power series representation (centered at a = 0) for the function below f(x) = = 1 1+x5…

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Q: 1) Discuss an uniform convergent, continuous ,integral, derivative sinnx for a series E n?

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Q: Evaluate the indefinite integral as an infinite series. ex – 1 dx | 7x ]) •c n = 1 8.

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Q: (b) The Maclaurin series of sinx is given by sin x=| 1! 3! 5! 7! Use the above expansion to check if…

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Q: What are the values of x that make the next series convergent (sin(x))" n n=1

A: To find the values of x for which the fpllowing series converges…

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Q: Find the sum of the convergent series.

A: Given, ∑n=1∞sin1n S=sin1+(sin1)2+sin13+.... it is a geometric series where: a=sin1,  r=sin1 we know…

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Q: Evaluate the indefinite integral using the series you found in problem 1₁ 1 1+x5 -dx

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Q: Find the first five non-zero terms of power series representation centered at x = 0 for the function…

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