because

evalc(cos(I*x));  # This assumes that x is real
convert(%, exp);
                                                cosh(x)
                                     (1/2)*exp(x)+(1/2)*exp(-x)

Use  extrema  command for this (gives min and max). Optimization:-Minimize  command gives the same result.

An example:

Download min.mw

See help on  CurveFitting:-PolynomialInterpolation  command.

A:=[[1,2],[5,7]]:
B:=[[1,2]]:
(convert(A,set) intersect convert(B,set))[];

# or

A:=[[1,2],[5,7]]:
B:=[[1,2]]:
({A[]} intersect {B[]})[];
 

p := [[[0, 5], [3, 10], [1, 20], [0, 50]], [[2, 5], [0, 10], [2, 20], [0, 50]]];
evalindets(p, list(numeric), i->`if`(i[1]<>0,i,NULL)) ;

evalc  command tries to bring the result to the form  a+b*I  , in which  a  and  b  are  reals.

evalc(I^I);
evalc(2^(2*I+6));

Apparently it should be regarded as a bug in Maple. Use  is  command instead:

is(a * conjugate(a) = abs(a) ^ 2);
                                                            true

Of course, Maple knows this identity, making a corresponding simplification:

simplify(a*conjugate(a));
                                                          abs(a)^2

Here is the corrected version:

Download proc.description_new.mw

f:=(x^2+y^2+2*y)^2-4*(x^2+y^2):
plots:-implicitplot(f, x=-4..4,y=-4..4, gridrefine=3);

# Or
algcurves:-plot_real_curve(f, x, y);

# Or (in polar coordinates)
simplify(subs([x=r*cos(phi),y=r*sin(phi)], f));
solve(%, r);
plot(%[4], phi=0..2*Pi, coords=polar);
 

restart;
Set:={R = 7.339698158, S = 2.378491488, W = 2.512047349}:
X:=eval(R, Set);
Y:=eval(S, Set);  #  and so on

You can do this in one line (multiple assignment):
restart;
Set:={R = 7.339698158, S = 2.378491488, W = 2.512047349}:
X, Y:=eval([R, S], Set)[];
 

Edit.

I think that in one answer it is easy to answer for everyone:

1. Student:-Calculus1:-LimitTutor command is very weak and just fails with this example.

2. For a student studying the theory of limits, it would be more useful to solve this example manually, first getting rid of the signs of the modules in the neighborhood of point  x=2  on the left and on the right.

3. The process of getting rid of modules is easy to automate with the help of Maple, after which the task becomes quite obvious:

Expr:=(2*abs(x-2)+abs(x+1)-3)/(abs(x^2-4)+x-2);  
A:=simplify(Expr) assuming x<2 and x>1.9;  # On the left
B:=simplify(Expr) assuming x>2 and x<2.1;  # On the right
plot(Expr, x=1..3, view=0..1, discont, size=[600,300]);  # A visualization
                        

restart;
SplitChange := proc(str::string) 
local start, i, len, k, L;  
start := 1; len := length(str); k:=0;
for i from 2 to len do 
if str[i] <> str[start] then k:=k+1; L[k]:=str[start .. i-1]; start := i end if;
end do;
L[k+1]:=str[start..len]; 
convert(L, list);
end proc:

Example of use:
SplitChange("WPKCPYWYYYXHYY");
                ["W", "P", "K", "C", "P", "Y", "W", "YYY", "X", "H", "YY"]

Edit.

A  and  B  are 2 curves on the surface  C :

restart; 
f:=(x,y)->2*x^2+3^2-x*y-4:
A:=plots:-spacecurve([1,y,f(1,y)], y=-2..2, color=red, thickness=3):
B:=plots:-spacecurve([x,1,f(x,1)], x=-2..2, color=blue, thickness=3):
C:=plot3d(f, -2..2, -2..2, style=surface):
plots:-display(A,B,C, orientation=[115,75], labels=[x,y,z]);

For this particular plotting, 20 digits is enough. It is better not to specify the global Digits, but to specify the desired accuracy when specifying the function itself. In this case, you need a procedural form for plotting:

restart;
f:= x->evalf[20](exp(x)*HeunC(2*x, 1/2, -1/2, -x^2, 1/8, 99/100)):
plot(f, 0..40);
                          

restart; 
a := plot(1/x, x=0..1);
op([3,2], a);   # This is the desired result