The function f(x)=4x^2arctan(x^4) is represented as the power series summation n=0 to infinity cnx^n? - cnx it
What is the power of x in the shortest time with a zero?
Find the radius of convergence of the series.
Please give a detailed explanation
Monday, December 28, 2009
Cnx It The Function F(x)=4x^2arctan(x^4) Is Represented As The Power Series Summation N=0 To Infinity Cnx^n?
1 comment:
Arctan (t) = integral (1 / (1 + t ^ 2))
Integral = (Σ t ^ 2n) n = 0,1,2, ...
Σ = 1 / (2n +1) * t ^ (2n +1) n = 0,1,2, ...
Thus
Arctan (x ^ 4) = Σ 1 / (2n +1) * (x ^ (4 (2n +1))) n = 0,1,2, ...
4x ^ 2 arctan (x ^ 4) = Σ 1 / (2n +1) * (x ^ (4 (2n +1))) (4x ^ 2)
Σ = 4 / (2n +1) x ^ (8N +6), n = 0,1,2, ...
You can see the answer to your first question, I ...
since the radius of convergence or arc tangent is 1 (this is due to the geometric sequence) .. it's also set the radius of convergence of the function.
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