Approximate sin 87° to four decimal places accuracy using an appropriate Taylor Series.

Q: Use power series operations to find the Taylor series at x = 0 for thefunctions x2 sin x

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Q: Obtain the half range sine series for ex in (0,pie)

A: We have to obtain half range for                                                        f(x)=ex  in…

Q: Obtain the half-range sine series for ex in (0,π)

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Q: Use substitutio to find the Taylor series at x = 0of the functions. e-5x

A: Given: The function f(x)=e-5x.

Q: Use the first three non-zero terms of power series to approximate | sin x dx.

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Q: Find the Maclaurin series for the functions sin 3x

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Q: find 5 th terms of the function{ sin(2x) }using Taylor series at a= pi/6

A: We will find out the required term.

Q: Calculate sin (0.3π) to 8 significant figures using the Maclaurin series expansion of sin(x). With…

A: Calculate sin (0.3π) to 8 significant figures using the Maclaurin series expansion of sin(x).

Q: approximate the value of cosine function of 58.9 degrees using the first 4 terms of the taylor…

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Q: Write the Taylor series for f(x) = sin(x) at n X= as Сп 2 2 n=0 Find the first five coefficients. CO

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Q: Please find a Taylor series for the function f(x)=6/(2-x) centered at x=1, using the Taylor series…

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

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Q: Use sigma notation to write the Taylor series about x = 8 for the function. 1 x +5 Σ k =

A: Taylor series of f(x) centered at x=a :           f(x) = ∑n=0∞ fn(a)n!(x-a)n =…

Q: Find the first few terms of the Taylor series centered at x 0 to evaluate: COS a - 1 lim

A: The Taylor series of cos x centered at x=0 is , cos(x)=1-x22!+x44!-x66!+… To evaluate limx→0cos…

Q: Find the Taylor series for cos x about a/3. Where is the series valid?

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Q: The power series that represents the integral | V1 + a3 da is:

A: The integral is ∫1+x3 dx. The series expansion of 1+xk is 1+xk=∑n=0∞knxn. Here, the function is…

Q: fu)=Sin(x) aニT R=?

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Q: Find the Taylor series and Taylor polynomials generated by ƒ(x) = cos x at x = 0.

A: given: f(x)=cosx as we know that the taylor's theorem is:…

Q: Use sigma notation to write the Taylor series about x = 7 for the function. 1 x + 5

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Q: r0.2 3 V dx 1+ x4

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Q: Find (a) Fourier Sine Series, and (b) Fourier Cosine series for the function f(x) = |x| , 0 < x < L

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Q: Approximate cos(0.2) to five decimal-place accuracy using the MacLaurin series for cos(x). cos(0.2)~

A: MacLaurin series of cosx is  cosx = 1- x2/2! + x4/4! - x6/6! + ......... We have to find the value…

Q: Use a power series to compute: sin(x?) dx =

A: We know that power series for sinx is sinx=∑n=0∞(-1)nx2n+1(2n+1)! So, power series for sin(x2) is…

Q: Obtain the 5th term of the power series of sin(x) for a value of x = 4.55.

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Q: Calculate sin(+0.06) to within 0.0001 (i.e. the size of the error must be less than 0.0001) by using…

A: Calculate sinπ4+0.06 to within 0.0001 by using the Taylor series about c=π4.

Q: Use sigma notation to write the Taylor series about x = 5 for the function. 1 x + 3 Σ k =

A: Taylor series

Q: Find the sum of the series Σ >x sin" (x). n=0

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Q: Use the exponential series to find an approximation to e-1 correct to three significant figures.

A: we know that,ex=∑n=0∞x2n!⇒ex=1+x1!+x22!+x33!+x44!+x55!+x66!+x77!+x88!+···putting…

Q: Determine the relative error when approximating e^-1 using fifth-degree Taylor polynomial with…

A: Firstly , we will write the 5th and 6th degree polynomial separately.  for x= -1, we can calculate…

Q: Find approximate value by using power series to three decimal places. 0.2 1 dx |

A: To evaluate∫00.2 e-x-1xdx

Q: 36. sin x?

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Q: • Derive the machurin series for f(x) = cesx. Then write down the Equation of the parabola that best…

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Q: Find the series expansion of sine over a half interval of the function

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Q: Use substitutio to find the Taylor series at x = 0of the functions. 5 sin (-x)

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Q: dx 4. Use a Maclaurin series to approximate with Jerrorf <0.005

A: The given problem is to estimate the definite integral using Maclaurin series with error 0.005, we…

Q: Find the power series for the function f(x) = e* using the power series for

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Q: State whether y =tan x can be expressed as a Fourier series. If so how?. If not why?

A: State whether y =tan x can be expressed as a Fourier series. If so how?. If not why?

Q: obtain the half range sine series for ex in (0,pie)

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Q: Use a power series to approximate the definite integral, I, t

A: Given, ∫00.2ln1+x5dx Let, I=∫00.2ln1+x5dx The power series expansion of lnx is…

Q: Find approximate value by using power series to three decimal places. 0.2 1 dx e

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Q: Use the Taylor series for sinh x and cosh x to verify that - sinh x = coshx. dx

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Q: Write the first 4 nonzero terms of the integral I= x sin(x)dx using the Maclaurin series for sin(y).

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Q: Use sigma notation to write the Taylor series about x = 9 for the function. 1 x + 5 Σ k

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Q: f (x) = sin(3x), а%3D0

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Q: Find the first 3 terms in the Maclaurin series for (a) sin²x, (b) V1- (c) xe¯*,

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Q: Use a series representation of sin 3x to find values of r and s for which (sin 3x lim + s) = 0. x2

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Q: By multiplying the Taylor series for ex and sin x, find the terms through x° of the Taylor series…

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