## 295 Reputation

16 years, 234 days

## odevity...

"Of those I looked at, all had Chinese authors. "

But I don't think this English term was invented by the Chinese.

## odevity...

"Of those I looked at, all had Chinese authors. "

But I don't think this English term was invented by the Chinese.

## Even and Odd...

Is the integral of (ax^2 + bx + c), from -5 to 5, equal to twice the integral of (ax^2 + c), from 0 to 5?

Consider the odevity of the functions.

(1) Since b*x is an odd function,  int(b*x,x=-5..5)=0.
(2) Since a*x^2+c is an even function, int(a*x^2+c,x=-5..5)=2*int(a*x^2+c,x=0..5).

## Even and Odd...

Is the integral of (ax^2 + bx + c), from -5 to 5, equal to twice the integral of (ax^2 + c), from 0 to 5?

Consider the odevity of the functions.

(1) Since b*x is an odd function,  int(b*x,x=-5..5)=0.
(2) Since a*x^2+c is an even function, int(a*x^2+c,x=-5..5)=2*int(a*x^2+c,x=0..5).

## Ok in Maple 8...

Yes, both work very well in Maple 8.
So my problem is completely solved.
Thank you very much.

plot(surd(x,3),x=-2..2,thickness=3);
with(plots): a:=1:
implicitplot(surd(x^2,3)+surd(y^2,3)=a^(2/3),x=-a..a,y=-a..a);

## Ok in Maple 8...

Yes, both work very well in Maple 8.
So my problem is completely solved.
Thank you very much.

plot(surd(x,3),x=-2..2,thickness=3);
with(plots): a:=1:
implicitplot(surd(x^2,3)+surd(y^2,3)=a^(2/3),x=-a..a,y=-a..a);

## surd...

Thank you, acer.

Using surd (which I don't know before) in Maple 8 can solve the second problem by the following code (which can produce the whole graph):

with(plots):
plot(surd(x,3),x=-1..1);

## surd...

Thank you, acer.

Using surd (which I don't know before) in Maple 8 can solve the second problem by the following code (which can produce the whole graph):

with(plots):
plot(surd(x,3),x=-1..1);

## How to solve it in Maple 8?...

Thanks. But how can I solve the problem in Maple 8?
It seems that Maple does not allow power functions with fractional powers or decimal powers to take negative values  even if they are defined there like y=x^(1/3)..

## How to solve it in Maple 8?...

Thanks. But how can I solve the problem in Maple 8?
It seems that Maple does not allow power functions with fractional powers or decimal powers to take negative values  even if they are defined there like y=x^(1/3)..

## Well, I see....

" the numpoints option just gives the plot routine a minimum for the number of points"

This made me better understand the meaning of the adaptive option. Thank you, Scott.

## Well, I see....

" the numpoints option just gives the plot routine a minimum for the number of points"

This made me better understand the meaning of the adaptive option. Thank you, Scott.

## Plotting regular polygons...

Thank you for your help. Your code is much simpler. Just  by controlling the number of points of a circle!

with(plots):
with(plottools):
R:=2:N:=7:
C:=circle([0,0],R,color=red):