I 've got huge problem with one more example. Didi anyone know hoe to find power series representation of the function: f(x)= -4x/ (1+2(x)^2)^2 Thank you all for all posible answeres
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Originally Posted by mauro21pl I 've got huge problem with one more example. Didi anyone know hoe to find power series representation of the function: f(x)= -4x/ (1+2(x)^2)^2 Thank you all for all posible answeres What is the integral of f(x)? (Hint: it is an arctangent). Thus, INTEGRAL f(x) dx= -atan(4x) Now, express, -atan(4x) As an arctangent series. Afterwards take the derivative term-by-term.
Originally Posted by mauro21pl I 've got huge problem with one more example. Didi anyone know hoe to find power series representation of the function: f(x)= -4x/ (1+2(x)^2)^2 Thank you all for all posible answeres Use the binomial theorem on 1/(1+2(x)^2)^2: -4x/ (1+2(x)^2)^2=-4x{1+(-2)(2x^2)+(-2)(-3)/2! (2x^2)^2+...} .........................=sum(n=0, inf) (n+1) (-1)^(n+1) 2^(n+2) x^(2n+1) RonL
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