• Support PF! Buy your school textbooks, materials and every day products Here!

Exponential function

  • Thread starter Kenji Liew
  • Start date
  • #1
25
0

Homework Statement



This topic is under linear system differential equation.Solve the system by using exponential method. Just want to ask the expansion of exponential function

Homework Equations



e^x=1+x+(x^2)/2!+(x^3)/3!+........

The Attempt at a Solution


then how about the e^(-1)=?
Besides what is the function of sin x and cos x in continued function (such in e^x)?
Thanks!
 

Answers and Replies

  • #2
537
3

Homework Statement


The Attempt at a Solution


then how about the e^(-1)=?
Besides what is the function of sin x and cos x in continued function (such in e^x)?
Thanks!
I'm not really for sure what your question even is. What problem are you trying to solve? Are you asking for the power series for sine and cosine?
[tex]\begin{align*}
\sin x &= x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots \\
\cos x &= 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots
\end{align*}[/tex]

Or are you asking for the following identities?
[tex]\begin{align*}
\sin x &= \frac{e^{ix}-e^{-ix}}{2i} \\
\cos x &= \frac{e^{ix} + e^{-ix}}{2}
\end{align*}[/tex]
 
  • #3
33,639
5,301

Homework Statement



This topic is under linear system differential equation.Solve the system by using exponential method. Just want to ask the expansion of exponential function

Homework Equations



e^x=1+x+(x^2)/2!+(x^3)/3!+........

The Attempt at a Solution


then how about the e^(-1)=?
Besides what is the function of sin x and cos x in continued function (such in e^x)?
Thanks!
e-1 = 1 + (-1) + (-1)2/2! + (-1)3/3! + ... + (-1)n/n! + ...
 
  • #4
33,639
5,301
Also, you have posted what appears to be the same question twice, which is frowned upon in this and most other forums.
 

Related Threads on Exponential function

  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
0
Views
940
  • Last Post
Replies
4
Views
7K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
820
  • Last Post
Replies
12
Views
7K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
19
Views
2K
  • Last Post
Replies
2
Views
1K
Top