Problem : Prove that (sin(x)) = cos(x) using the Taylor series of the two functions.
Since
sin(x) = x ^{2n+1} |
(sin(x)) | = | x ^{2n+1} | |
= | x ^{2n} | ||
= | x ^{2n} | ||
= | cos(x) |
Problem : Prove that 1/(x + 1)dx = log(x + 1) using Taylor series. (The Taylor series for 1/(x + 1) is (- 1)^{n} x ^{n} .)
We have
dx | = | (- 1)^{n} x ^{n} dx | |
= | x ^{n+1} | ||
= | log(x) |