Question

In 18.01 Excercises by Prof. David Jerison
unit 1 Differentiation
1A-3 how do you identify a function as odd,even or periodic

Answer 1

A)\[x ^{3}+3x/1-x ^{4}\]
B)\[\sin^{2}x \]
C)\[\tan x/1+x ^{2}\]
D)\[(1+x)^{4}\]

Answer 2

http://en.wikipedia.org/wiki/Even_and_odd_functions
if f(x) = f(-x) then the graph has symmetry with y axis and is an even function (the power of the function is even, e.g. x^2)
if -f(x) = f(-x) then the graph has symmetry around origin and the function is and odd (the power of the function will alsy be odd, e.g. x^3).
Not sure about the periodic other than the function contains one or more of the periodic functions.

Answer 3

thanks,i see that
if \[f(x+p)=f(x)\] for all x values in a set of domain,where p is a positive constant,then f is called a Periodic Function and the smallest such number p is called a period.For instance \[y=sinx\] has a period \[2pi\]
so trigonometric graphs are periodic graphs.
Thanks again...