what do know about periodic functions ? Are constant function periodic e.g. F(X)=1000 .Also answer that e^(-x) ,where ( ) stands for least intger function is periodic , continous differentiable even function or not.go thru its graph.
2006-08-09 03:00:51 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Well........ I guess I know a little bit about periodic functions.
A 'periodic function' is one that 'repeats itself' in the sense that
f(c) = f(c+k) = f(c+2k) = ∙∙∙∙ f(c+ nk)
where c and k are both constants (k is called 'the period' or 'periodicity' of the function and must be unique) and n can be any positive integer (for many periodic functions, n may also be negative)
For example, the sin function is periodic since
sin(π/4) = sin((π/4) + n*2π) = .5√2
where n can be any integer and the period is 2π.
From the definition it might be tempting to say that a constant function is periodic, but it isn't since it has no unique period.
The function e^(-x) isn't periodic since e^(-x+k) doesn't equal e^(-x) for any integer value of k.
e^(-x) can't possibly be continuously differentiable since the the least integer function is discontinuous at every integer value of x.
e^(-x) would 'look like' a series of 'stairsteps' that descended along a curve from left to right.
Hope that helps.
Doug
2006-08-09 03:29:38 · answer #1 · answered by doug_donaghue 7 · 1⤊ 0⤋
I am not very sure, but I think constant functions are periodic with a period of infinity.
In fact all non-periodic functions can be treated as periodic with infinite periods. That, if I remember well, is the link from Fourier Series to Fourier Transform.
Somebody please correct me if I'm wrong.
2006-08-09 03:22:13 · answer #2 · answered by Anonymous · 0⤊ 0⤋
A "periodic" function is just as it says...
A linear function, such as e^(-x) or f(x) = 1000 is not periodic.
f(x) = 1000 is constant as you said, e(-x) is not as it changes depending on the value of x.
Examples of periodic functions are the trigonometric functions...
sine, cosine, tangent, cotangent, cosecant, secant... These are all periodic functions.
2006-08-09 03:25:47 · answer #3 · answered by AresIV 4 · 0⤊ 0⤋
Altough constant functions are said to be periodic but they don't have a fundamental period.
F(x)=e^(-x) is neither a periodic function, nor continuous & hence not differentiable.
F(-x)=e^(x), which is not equal to F(x). Hence, it's not even also.
2006-08-09 03:25:18 · answer #4 · answered by Kashish 1 · 0⤊ 0⤋
no constant functions are not periodic nor is e^(-x)
examples of periodic functions are sine function,cos function etc.
2006-08-09 03:09:04 · answer #5 · answered by raj 7 · 0⤊ 0⤋
i am 17 a commerce student > i dont know. Which standard science or maths is this?
2006-08-09 03:08:46 · answer #6 · answered by dudeshubham 2 · 0⤊ 0⤋
dude im seriously a junior to answer that type of question
2006-08-09 19:16:13 · answer #7 · answered by shailesh 1 · 0⤊ 0⤋
Uhh yeh...
2006-08-09 04:27:52 · answer #8 · answered by Anonymous · 0⤊ 0⤋