Consider the algebraic equation, tanx – 1 = 0 (i) If f(x) = tanx – 1, find f'(x) (ii) Find the recursive relation for {x„} to approximate the root, by taking the initial approximation as, x, = 2 (ii) Generate the sequence {xn} by writing at least the first 10 terms.

Q: Find Fourier sine series of f(x) = 4x on - L≤ x ≤ L

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Q: 1. Find the Fourier series of the function: f(x) = |x| in the period of -n<x<

A: Fourier series formulae: f(x)=a02+∑n=1∞ancos(nx)+bnsin(nx)a0=1π∫-ππf(x)dxan=1π∫-ππf(x)…

Q: The interval of convergence of Ln=0 +0o 2(x+7)" -105x-4 -10kxS-4

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Q: Can the iteration xn+1 = cos (xn) be used to find the solu- tion of the equation cos (x) – x = 0 in…

A: Solution is given below

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0. ƒ (x) has a root in [0]. To solve…

A: The given function is                     f(x)=cos x-3x+1 Also given that the fixed-point iteration…

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () <0. f(x) has a root in [0]. To solve…

A: Given : function      fx=cosx-3x+1 and the fixed point iteration      xn=gxn-1 where gx=131+cosx…

Q: sin x-x Evaluate the limit lim using a Taylor Series x→0

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Q: Consider the function f(x) = cos x - 3x + 1. Since f(0)f < 0, f(x) has a root in [0,. To solve f(x)…

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Q: 4. Find the half-range Fourier cosine series for the function f(x)=sin-x in the range 0<x<T Sketch…

A: If the function is over half 0 to L then it is half range Fourier  series the half range Fourier…

Q: 18 Given the power series F(x)= 2 (-1)" (x-3)" n= 0 2" Find the derivative for the power series…

A: Answer to the question as follows:

Q: -π<x 0. 0<x<π. 2 f(x) = {?

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Q: Find the Fourier series of the function f on the given interval. f(x) = 7 - 4x, -n <x < T 00 f(x) =…

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Q: Determine the half-range sine series for the function defined by: x, 0<x < f(x) = 0, %3D <x < T 2-

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Q: (2x, if 0sxs2, Expand the function f(x)= < in the Fourier sine series. Find x+2, if 2<xs3 the value…

A: The function is fx=2x,        if 0≤x≤2x+2,    if 2≤x≤3. The odd extension for this function is gx=fx…

Q: Find the half-range sine series of f(x) = ex on [0, 1]

A: The half-range sine series of a function f(x) on an interval 0,a is given by, fx=∑n=1∞ bn sinnπxa…

Q: The first derivative of the power series 9 9x2 9x3 9x4 f(x)=9+ .. is 1! 2! 3! 4! O -9 f(x) O f(x)…

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Q: Find Ln(0.98) by Maclaurian series F(x)=Ln(X+1)

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Q: 2. Determine the Fourier series for F(x) = -2 when F(x) = 2 when -π<x<0 0<x<T

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Q: 2. Use differentiation to find a power series representation for f(x) = (1+x)²·

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Q: Q1: Find with sketch the Fourier coefficients and Fourier series of the function f(x) defined by…

A: Introduction: A Fourier series is a sum of sine and cosine waves that represents a periodic…

Q: Find Fourier series for the function f (x) = x\,- <x< T

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Q: cos (6x4) – 1 Let f(x) Evaluate the 9th derivative of ƒ at x = 0. %| x7 f(9)(0) = Hint: Build a…

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Q: ∑ ∞ n=1 sin(1/2n) − sin (1/2n + 1). Does this converge or diverge? I believe it diverges by direct…

A: The given series is: ∑n=1∞sin12n-sin12n+1

Q: 2. Use differentiation to find a power series representation for f(x) = 1 (1 + x)² °

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Q: 4. Find the half-range Fourier cosine series for the function f(x)=sin-x in the range 0<x<n Sketch…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: . Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (²) < 0, ƒ (x) has a root in [0]. To…

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Q: Express f(x) = n + x_for -<x<n as a Fourier series.

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Q: Using Taylor polynomials of ln (x + 1), calculate an approximation of ln (2) with an error less than…

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Q: (b) Obtain half range fourier sine series for f(x) = r,0<x <3

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () <0. f(x) has a root in [0]. To solve…

A: Given f(x)=cosx-3x+1

Q: 0o COS 17. Determine whether 2 converges or diverges. Evaluate it if is convergent. dx 18. Determine…

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Q: f(x) = π-x,-π<X<π

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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: Date... Q. Find the Fourier Series o x)--x-X

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Q: 2. Sketch the graph of f(x)=-x, 0<x<*, f(x)=f(x + 2). Then, find the Fourier sine series of f(x).

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Q: 9. Use numerical integration to find the first ten terms in a Fourier series for the function sin x…

A: Given: The Fourier series includes the numerical integration being the function of sin x2 that…

Q: :Q6-. Find the Fourier series for the function below S 0, -A < x < 0 S (æ) = { f(x) and has period…

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Q: Find the Fourier series for the periodic function: if - 1<x<0 f(x) = {2 if 0<x< 1 f(x + 2) = f(x)

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Q: 4. Expend the given function in the Fourier series in the given interval [5x-1, -A <xs0 f(x)=.…

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Q: If f(X)=1/2*(π-x), find the Fourier series of period 2π in the interval (0,2π)

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Q: 4. Find the Fourier series for the Function f(x) = |x| ,When -n< X<n.

A: The given function is: f(x)=|x| ;          -π≤x≤π Therefore: f(x)=-x            if  -π≤x&lt;0   xif…

Q: 4. Express the f (x)=1+x function as a Fourier series in the interval of -T<x<T (Plesae check first…

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Q: Determine the Fourier Series of the function below: * f(x) = x, over the interval - < x < 7 and has…

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Q: Obtain the Fourier series expansion for the function of period 2π as follows f(t)=2-t/π,   -π<x<π.

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (-) < 0, f (x) has a root in [0]. To solve…

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Q: Determine the Fourier series for the function defined below: f(x) = 2x in the range x = 0 to x = 2pi…

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Q: Find the Fourier series for x2  in the interval 0 ≤ x ≤ π

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Q: Find the Fourier Series for f(x) = x

A: Use the Fourier series standard formula then find the coefficients.

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.