1. ## Well behaved functions

which of the following are not well behaved funtions:
a)ax^2 + bx+c
b)e^x for all x
c)y= |x|
d)g(x) = cosx + sinx for -pie=< x =< pie and 0 elsewhere

2. Originally Posted by myoplex11
which of the following are not well behaved funtions:
a)ax^2 + bx+c
b)e^x for all x
c)y= |x|
d)g(x) = cosx + sinx for -pie=< x =< pie and 0 elsewhere
"Well-behaved" is a term mathematicians use because they are lazy to state all the conditions a function must meet. Hence this term is not well-defined. You need to say what it means over here.

3. Originally Posted by myoplex11
which of the following are not well behaved funtions:
a)ax^2 + bx+c
b)e^x for all x
c)y= |x|
d)g(x) = cosx + sinx for -pie=< x =< pie and 0 elsewhere
(sigh)
Would you eat $\displaystyle \pi$? No. So don't spell it "pie," spell it correctly: "pi."

Okay, this might be what you need: $\displaystyle y = |x|$ is not "smooth." That is to say all the derivatives of y are not continuous. (In fact no derivative of this function is continuous.) In this sense $\displaystyle y = |x|$ is not well behaved.

-Dan

4. Originally Posted by myoplex11
which of the following are not well behaved funtions:
a)ax^2 + bx+c
b)e^x for all x
c)y= |x|
d)g(x) = cosx + sinx for -pie=< x =< pie and 0 elsewhere
Originally Posted by topsquark
(sigh)
Would you eat $\displaystyle \pi$? No. So don't spell it "pie," spell it correctly: "pi."

Okay, this might be what you need: $\displaystyle y = |x|$ is not "smooth." That is to say all the derivatives of y are not continuous. (In fact no derivative of this function is continuous.) In this sense $\displaystyle y = |x|$ is not well behaved.

-Dan
d) is not even continuous at +/- pi

RonL

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### well behaved function sinx

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