find a power series for the given function, centered at a=0. a)F(x)=ln(3+x) b) G(x)=1/(1+2x)^(1/4) c) Integral, 0 to x, (1-cos(t)/t^2) dt
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You can use Taylor's formula, but I'd use the geometric series for the first one. now integrate wrt x.
Originally Posted by matheagle You can use Taylor's formula, but I'd use the geometric series for the first one. now integrate wrt x. although i didnot have mathematics as honours in college i didnot understand one thing: How can ln(3+x) be expressed as 1/(3+x).
Originally Posted by Pulock2009 although i didnot have mathematics as honours in college i didnot understand one thing: How can ln(3+x) be expressed as 1/(3+x). . So . So if you have a power series for , integrate it, then you will have a power series for .
Originally Posted by twofortwo find a power series for the given function, centered at a=0. a)F(x)=ln(3+x) b) G(x)=1/(1+2x)^(1/4) c) Integral, 0 to x, (1-cos(t)/t^2) dt a)F(x)=ln(3+x) =ln(3(1+x/3)) =ln3+ln(1+x/3) =ln3+(the standard logarithmic expansion)
Originally Posted by Prove It . So . So if you have a power series for , integrate it, then you will have a power series for . that makes a lot of sense!!!thanks!!
Originally Posted by twofortwo find a power series for the given function, centered at a=0. a)F(x)=ln(3+x) b) G(x)=1/(1+2x)^(1/4) c) Integral, 0 to x, (1-cos(t)/t^2) dt b)G(x) can be expanded binomially to get a power series if i am not wrong.
Originally Posted by Pulock2009 b)G(x) can be expanded binomially to get a power series if i am not wrong. Yes, as long as you write it as .
Originally Posted by Pulock2009 although i didnot have mathematics as honours in college i didnot understand one thing: How can ln(3+x) be expressed as 1/(3+x). I clearly said you should now integrate.
thank you!! i understand all of them except the integral one. can i get more help on that one please! Thanx so much!
Originally Posted by matheagle I clearly said you should now integrate. Yes you did, the OP just didn't understand WHY you should integrate, hence my fill-in post.
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