Evaluate the indefinite integral as an infinite series
Integral of sinx/2x
Find the first five non-zero terms of series representation centered at x=0.
What is the radius of convergence?
Need Step by step to understand please. Thanks
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We know that the Maclaurin series for sine is given by:
sin(x) = Σ(n=0 -> infinity) (-1)^n * (x ^ (2n+1))/(2n+1)!
= x-x^3/3! + x^5/5! - x^7/7! + ...
Substituting this into the expression sin(x)/(2x), we get:
sin(x)/(2x) = 1/2 - x^2/(2*3!) + x^4/(2*5!) - x^6/(2*7!) + ...
and then you can integrate this easily since it is just a polynomial.
You can then write out the first 5 terms to get the series
representation for f(x) = sin(x)/(3x) .
R is infinte
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