Problem :
Prove that
(sin(x)) = cos(x)
using the Taylor series of the two functions.
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
.)
dx
|
= |
(- 1)n
x
n
dx
|
|
| = |
x
n+1
|
||
| = | log(x) |
