26th Derivative of a Function

  • Thread starter Frillth
  • Start date
The problem statement, all variables and given/known data

Given that f(x) = sin(x) for x =/= 0 and f(x) = 1^x for x=0, find the 26th derivative of f at 0. Hint: can you find a power series for f(x)?

The attempt at a solution

I have no idea how to solve this problem. Since 1^x is always 1, the first derivative at 0 is 0, so ALL derivatives must be 0, right? I'm confused as to how a power series even comes into play in this problem.
 

StatusX

Homework Helper
2,564
1
That's a very strange defintion. Note that f(0) is just a number, so all they had to say was f(x)=1 for x=0, the 1^x bit is superfluous. But moreover, the function is not continuous at x=0, so doesn't have any derivatives, let alone 26. Which leads me to ask, are you sure you copied the question correctly?
 
I just noticed that somebody erased a line in my book! It should have been sin(x)/x for x=/=0 and 1 for x=0. That makes a lot more sense.
 

arildno

Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,846
130
I advise you to use the hint given!
 

Want to reply to this thread?

"26th Derivative of a Function" You must log in or register to reply here.

Related Threads for: 26th Derivative of a Function

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top