What is Piecewise function: Definition and 103 Discussions
In mathematics, a piecewise-defined function (also called a piecewise function, a hybrid function, or definition by cases) is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. Piecewise definition is actually a way of expressing the function, rather than a characteristic of the function itself.
A distinct, but related notion is that of a property holding piecewise for a function, used when the domain can be divided into intervals on which the property holds. Unlike for the notion above, this is actually a property of the function itself. A piecewise linear function (which happens to be also continuous) is depicted as an example.
I was going through trying to solve various Fourier problems, and I came across this one.
f(x) = \left\{\begin{array} {c}0 \ \ \mbox{for} \ \ - \pi <x<0 & x \ \ \mbox{for} \ \ 0<x<\pi
Here is how far I have gotten, using that
a_n = \frac{1}{\pi} \int_{- \pi}^{\pi} xcosnx dx
and
b_n =...
Hello,
Here is a piecewise function that I came over, and it does not seem to have a definite answer, and so I beg of your recondite knowledge to guide me on this one:f(x) =
ax^2 + bx + c if -oo < x < 0
d if x = 0
[(x^2)(sin(1/x))]-2 if 0 < x < oo
Find all...
hi,
i have been working on an Options assignment, and i have this formula as one of my answers:
X_{t}=\left\{\begin{array}{cc}X_{t-1},&\mbox{if } S_{t} < S_{t-1}\\aS_{t},& \mbox{if } S_{t}\geq S_{t-1}\end{array}\right
where a is a constant. the question however asks for a "single...