Please have a visit of this qestion `http://math.stackexchange.com/q/574843/8581`. I did a very elementary attempt there for example for a function:

 > with(plots):
      h := x->piecewise(x < -2, x+3, x <= 2, 5-x^2, 3-x):
      t:=x->h(-x):
      a:= plot(h(x), x = 0 .. 10, color = red, thickness = 3):
      b:= plot(t(x), x = -10 .. 0, color = green, thickness = 3):
      display(a,b);

But  I am eager to know  the formal codes if they exists. Thanks for your time.

I am so thankful if there are any hints about this question:

http://math.stackexchange.com/q/523048/8581

Generally, can we check the existence of a valid limit by using epsilon-delta method in Maple?

Thanks

Today, I was working on a problem in the class which said:

if f(x)=ax^2+b, x<=1 and 1/x, x>1; then find the values of "a" and "b" such that f'(1) be defined. I checked it to be continuous at x=1 first and so I got a+b=1. Secondly, I wanted to get another equation, so I checked the differentiability of the function by the definition of derivation at x=1, so:

[> f := x-> piecewise(x <= 1, a*x^2+b, 1 < x, 1/x);
> limit((f(x)-f(1))/(x-1), x = 1, right);

Recently I saw this question (http://www.mapleprimes.com/posts/141668-Partitions-Of-A-Natural-Number-Into-Factors). I want to find the divisors of a number, say 120, :

2,4,6,8,10,12,15,20,24,30,40,60,120

for the students but couldn't find a simple way for that expect the solutions in above link. Isn't an easier way to do this job in Maple?

Thanks so for the time

Here is a solve problem based on theoritical analytic approach, http://math.stackexchange.com/q/460365/8581. May I ask make me hints in which I can visualze the region f maps. In the question we are speaking about $f(E)$, so I am thinking about a plot illustaring $f(E)$. Thanks for the time and any hints.