find the taylor series for f(x)=sin(x) centered at c=pi/2 on what interval is the expansion valid in interval notation

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.

Q: Find the Fourier series for the etion fon) = |x\, -2{*<! %3D what happens at x==2 and x=0 ?

A: Period  T =3 Frequency  ω=2πT=2π3 a=-2, b=1 The Fourier series is a0  +    ∑K=1∞ ancosKωx+bnsinKωx…

Q: Use the Taylor series for 1/ (1 - x2) to obtain a series for 2x/ (1 - x2)2.

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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.

Q: 2 11 { 6 1 if - <a < 0 if 0 < x < n

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Q: Show a representation of f(x) = cos(x) using the sum of it taylor series at the center

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Q: Find the taylor series for f(x) = -4ex about x=5

A: The Taylor series of a function f(x) is given by  f(x)=∑n=0∞fn(a)n!(x-a)n Here, the given function…

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: Example Calculate third order using Taylor series for f(x)= sin(x), at X=2, using Xo= 0 ?

A: Sinx taylor series.

Q: Differentiate the Maclaurin polynomial of degree 4 for f(x) = ex . Describe the relationship between…

A: Maclaurin polynomial of degree 4 is P4x=f0+f'0x+f''02!x2+f'''03!x3+f404!x4.

Q: Find a Taylor series expansion around x = 2 for f(x) = ln x

A: To find the Taylor series expansion for f(x)=ln(x) around x=2 is given by :-

Q: 1) Find the Taylor Series for sin(x)

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

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: Write the Taylor series for the function of two variables in which fourth derivative involve ?

A: Taylor series of a two variable function : Let us  suppose f(x,y) be a two variable function on R…

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: Find the Fourier series for the function f(t) = t² on the interval [—^, ^]. Use the result to find…

A: The given problem is to find the Fourier series representation for the given periodic function…

Q: What is the 7th term in the Taylor series for f(x) = 5e5* taken about x 7th term = 7-6-5-4-3-2-1-36…

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