5) Obtain the three-point central difference formula for the second order derivative with a remainder by using the Taylor series expansion. Calculate f"(3) by using this formula for the data given. Firstly, write Taylor series expansion for f (x) around xo. Also, find the exact value of the f"(3). 1 2 3 4 Ax) 34 102 228 Solution 5) Taylor series expansion for fAx) around xo:

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Q: Q5: a\. Let f(x) = x³ - 3x² -1, x ≥ 2. State and prove the theorem of derivative of inverse…

A: Here , f(x) = x3-3x2-1 We find required value.

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Q: 3. Find Taylor series for tan-1x about x =1 .

A: We find the Taylor series for tan-1x about x=1.

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Q: Write the first three terms of the Taylor series for f(x) =Vx at a = 1. Show your reasoning

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Q: 00 4n 6(-7)"x

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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…

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Q: etermine the Taylor series of the function f (2) = (3+ x) around x = 1. 00 Š(-1)"4"(z - 1)" b)…

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A: Since you have posted multiple questions, according to our guidelines we have done first question…

Q: 1. A power series is a series of the form and cn's are where x is a 2. The power series can be…

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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: Part A) Use the Taylor series expansion of sin x to write sin(√(t)) = t^(1/2) - (t^3/2)/3! +…

A: We see the Taylor series expansion of sin x to write sin(√(t)) = t^(1/2) - (t^3/2)/3! + (t^5/2)/5! -…

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:

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Q: 2012 N Q3 (i) Given that 2-3 5y i) Given also that = 25 , find the value of x and of y. 125x-2

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