Q3(a) Find the length of the curve, x5 1 y : 5 12x3 1

Q: Write the Taylor series for f(x) = sin(x) at x as 3. Cn x 3 n=0 first five coefficients.

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Q: Solve the initial value problem using a power series. y" + 1xy' - 4y = 0, y(0) = 9, y'(0) = 0.…

A: Please see the attachments

Q: 4. Find a power series representation of the function f(x)=arctan(x) centered at x= 0.

A: Topic = Series

Q: Use differentiation to find a power series representation for 1 f(x) = (7 + x)² ' x) = Σ n = 0

A: Given that The formula for power series expansion is, To find the power series expansion let's…

Q: The first derivative of the power series D (-1)" (2x)" is n! f(x) = n=0

A: Given : fx=∑n=0∞-1nn!2xn As    e-ax=∑n=0∞-1nn!axn∴e-2x=∑n=0∞-1nn!2xn Therefore, fx=e-2x   .....1

Q: Find the radius and the interval of convergence of the power series (3x + 1)7+1 and evaluate its…

A: Here we have to use Ratio Test.

Q: Q1): use Binomial series to find the first four terms of the function: dx V1– x2

A: Since you have posted multiple questions. I am answering the first one. Please post the question…

Q: sinx at x = n is given by The Taylor series expansion of X - T

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Q: Obtain the term of the power series of sin(x + 1) where n = 3 for a value of x = 3.20.

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Q: d Evaluate the differential dx of the series at x = 1rad. (x2 sin knx) where k> 0. Determine also…

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Q: 5. Find the coefficient of (x – )' in Taylor series about of y = sinx

A: The given function is: y=sin x Now Taylor series of y(x) about x=π4 is given by:…

Q: What is the 1st term in the power series expansion of the function y = cos x?

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Q: Use substitution to find the Taylor series at x = 0 of the function 22 sin (- x). ...

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

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Q: 3. For what values of x , does the series, 1-(x- 4)+ - (x – 4)* --(x - 4} + . + 1 (x – 4)² 4 1 (x –…

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Q: 1. A) Express 0 1 4 1+x dx as a power series.

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Q: Evaluate 1 dx 1+ x4 as a power series centered at 0. Write out the first four nonzero terms (not…

A: We know that the sum of geometric series 11-x=1+x+x2+x3+..... similarly, we can write for 11+x4…

Q: fu)=Sin(x) aニT R=?

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Q: 3. Find the derivative of the series (-1)**'2" -x2n+3 n=0 n!

A: We are authorized to solve only 1 question, please repost remaining questions

Q: Q1: (a) Estimate the value of the function f(x) = e²x at x = 1.5 using a Taylor's series expansion…

A: here i used Taylor's Expansion to solve this question.

Q: 10. Given that y = sin-1 2x. Show that (1 - 4x2) d²y = 4x dy dx? dr Find the Maclaurin series for…

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Q: Find a series expansion centered at x = 0 for tll sin(t)dt. Σ n=0

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Q: 4. For the function f(x) find the power series representation and its interval of (1 – 4x)²…

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Q: Expand f(x) = tan-1x in a Taylor series about x= 0 and use this Taylor series with n= 3 to…

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Q: Q9: Use the power series method to solve y" + y = 0 near x = 0.

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Q: Find the Taylor series for f(x) = ln(1+4x) about x = 0 by taking derivatives. Σ n=1 Compare your…

A: Here, f(x)=ln(1+4x)

Q: Solve for the power series about x=0 (x² + 5)y" - 2y = 0

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Q: Verify F (1,1; 2;x) = –x¬ln(1 – x) By expanding each function in a power series about x = 0.

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Q: Find the Taylor series for y = sin xr about a = t/ 2. What are two applications of series…

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Q: A. Use power series to solve (1 – x)y' - 2y = 0

A: In the question we have to solve the differential equation using power series.

Q: Find the power series for f(x) = ln(1 − x) centered at x = 0 by using term-by-term integration or…

A: Given  fx=ln1-x

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

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Q: Use Taylor series to write the expansion of f(x)=cos(3x) at x=0?

A: Taylor series expansion of f(x) is given by:

Q: x(х — 2)у" — бу %3D 0 about x =1

A: Given differential equation xx−2y''−6y=0 We have to find the power series solution of xx−2y''−6y=0…

Q: Find the half range sine series for f(x) = x( - x) in (0, 1).

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Q: The series ∑Cn(x+9)^n converges at x=−4 and diverges at x=−17.

A: We know that if the power series ∑ n=1∞an (x-b)n is convergent at x=a, then this series is…

Q: 1 dx o 1+x3 1/2

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Q: 2. Obtain the Taylor's series expansion of log(cosx) about x = 7% upto the fourth degree.

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Q: If y =1+2x + 4x² + 8x +... i) Show that x= y -1 2y i) Find the interval in which the series is…

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

A: We know that the power series representation (centered at a=0) for the function ft=11+t is given by…

Q: Q1. (a) Estimate the value of the function f(x) = e²x at x = 1 using a Taylor's series expansion of…

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Q: Use Taylor series for y(x + h), y(x – h), y(x + 2h), and y(x – 2h) to derive the FD formula for the…

A: Here we have to use taylor series for y(x+h) , y(x-h) ,y(x+2h)  and y(x-2h)

Q: Q1): use Binomial series to find the first four terms of the function: dx V1- x2

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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…

Q: The Maclaurin series of sinx is given by sinx = 1! +.... 7! - 3! 5! Use the above expansion to check…

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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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Q: Compute the value of the improper integral. (If the integral diverges to co, type oo; if 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(3x).…

A: We need to find polynomial series.

Q: Find the first three nonzero terms of the Maclaurinseries for function and the values of x for which…

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