Aleslavid Gan ESIFIS 7.5 (continued) 8. f(x) = sin(x) c = = ₁ F(x)=sin(x) f(x) = cos(x) f(c) = f '(c) = = f'(x) = - Sin(x) ƒ^ ( ² ) = = √2/² f"(x) = -cos) f" (c) = -√² f"(x) = sin(x) f" (c) = √2 प WIGG 2 + √2/2² (× - - 2 × 5) ² - 2!

Q: For f(x) = 3 + 7x - 19(x^2) + 2(x^4) find the maclaurin series (Taylor series about x =0) Please do…

A: The Solution is given below:

Q: 8. Find the Taylor series of f(x) = sin(x4) about x = 0. = 9. Using the first five terms of the…

A: 8. We have to find the Taylor series of fx=sinx4 about x=0. 9. Using the Taylor series to calculate…

Q: Find the series solution of y" + xy' + y = 0. Show all the work.

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Q: A B Convergent Divergent Use the ratio test to determine whether the series converges. 5+k

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Q: 12 2) 18 27 *19

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Q: Expand f(x) = cos 0 < x < π, in 3. a Fourier sine series. In addition, indicate when the Fourier…

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Q: Solve for the value of f(x) = e3*x4 Using 11 term Taylor series if x = 0.05X

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Q: Find a power series for the function 3 f(z) = 5- 2r and determine its interval of convergence.

A: from geometric series,

Q: #3. Prove that 2 = tan [ = log (T_-_ iz)

A: To Prove:z=tan1ilog1+iz1-iz12.

Q: rĩ sec² 0 (e) tan 0 do. Vtan 0

A: That's easy. Have a great day!!!

Q: 18. Find the Fourier sine series in (1/3, for 0<x<T|3, f(x)= 0, for /3<x<2r/3, (-7/3, for 2n/3<x<n.…

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Q: 6. (a) Calculate the Fourier Series of f(x) = |x], −1 < x < T. (b) Draw the 2-periodic function…

A: According to the Bartleby guidelines, I will answer first three subparts of a multiple subpart…

Q: Find the Taylor Series of f(x) = cos centered at a = 2 *. Find the interval of convergence. Show all…

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Q: 7a) Find the first four derivatives of f(x) = and evaluate at x = 1. 7b) Find a formula for the nth…

A: We are given : f(x)=1x2⇒f'(x)=-2x3⇒f''(x)=(-2)(-3)x4=6x4⇒f'''(x)=-24x5⇒f''''(x)=120x6Now, at…

Q: Problem 11. For this problem you may use the fact that the Taylor series of cos(I) centered at zero…

A: problem111. use the Taylor series of cos x to find the first 5 non-zero terms in the Taylors series…

Q: Write the nth term ( general term) for these Maclaurin series  1) (e^x)(cosx) 2)(e^x)(sinx)

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Q: Find the third Taylor series for f(x) = 2^-x about 0. Use this series to evaluate the function at…

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Q: Find a power series representation for x2cos(2x) and then by differentiation, show tat the equation…

A: Power series exaption of the function

Q: Problem 10. The power series from the previous problem is the Taylor series for f(a) = e. 00 p(x) =…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one .…

Q: Construct the Taylor series of f(x) = sin(x) centered at π. Determine how many terms are needed to…

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Q: etermine the coefficients of the x3 term of the Taylor series about the point 0 of the function f(x)…

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Q: 3.7 Prove that the real trigonometric series (an cos nx+b,sin nx) con- verges in L2(-T, 7) if, and…

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Q: expand the function f(x) = sin(x) / (coshx +2) in a taylor series around the origin going up to x^3.…

A: Taylor series of function f(x) around x=a is defined as:

Q: Q2: Based on series solution of Legendre Equation (1-x)y"- 2xy'+ ((l+1)y=0 Find Legendre Polynomial…

A: We solve this using power series of differential equation

Q: What is the next term in the Taylor series generated by cos x after 24 (Simplify your answer. Use…

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Q: Find the first 4 terms of Maclaurin series for f(x) = sinx+ ln(cosx). Find the error we make when we…

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Q: 1.3 Verify that f d = xp= x2V1+ x2 V1+ x² +c using the method you were taught in this course.

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Q: Find the Taylor Series generated by f(x) = (7 · X) ² at X=6 : f'(x) =__9 (7-X) 10 90 ƒ"(x)= (7-x)"…

A: The given function is fx=17-x9 centered at x=6