Register to reply

26th Derivative of a Function

by Frillth
Tags: 26th, derivative, function
Share this thread:
Frillth
#1
Dec16-06, 11:17 AM
P: 80
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.
Phys.Org News Partner Science news on Phys.org
Hoverbike drone project for air transport takes off
Earlier Stone Age artifacts found in Northern Cape of South Africa
Study reveals new characteristics of complex oxide surfaces
StatusX
#2
Dec16-06, 11:38 AM
HW Helper
P: 2,566
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?
Frillth
#3
Dec16-06, 11:45 AM
P: 80
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
#4
Dec16-06, 12:24 PM
Sci Advisor
HW Helper
PF Gold
P: 12,016
26th Derivative of a Function

I advise you to use the hint given!


Register to reply

Related Discussions
Derivative of function Calculus & Beyond Homework 5
Derivative of a function with ln Calculus & Beyond Homework 7
Derivative of a Function Calculus & Beyond Homework 5
Derivative w.r.t. a function Calculus 9
(Old) Lee Smolin presentation Oct. 26th, 2006 Beyond the Standard Model 1