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- Problem 1:
- How many different values can the following expressions take on if parentheses are added?
2*3+4/5
2^3^4+5
- Problem 2:
- In Maple, what are the results of the following commands?
> Digits:=3:
> 1010 + 3;
> 1010 + 3.0;
> 51.3 + 1.05;
- Problem 3:
- In Maple, what is the output of the following command?
> a := 'a': subs( x=2, a*x+3*x^2 ); # those are right-quotes
- Problem 4:
- Exactly what commands would you type into Maple in order to find out how many terms are in the polynomial (x^4 + x^2 + 1 )^250? Briefly explain what steps your commands perform.
- Problem 5:
- In Maple, enter the commands
> x := 2: y := 3:
> z := 'x' + y: # Those are right-quotes.
> x := 4:
> z;
What is the output from the last command?
- Problem 6:
- Part (a): In Maple, what is the value of y if
> y := `2+2` + 2; # Those are left-quotes.
- Part (b): In Maple, what is the value of y if
> y := '2+2' + 2; # Those are right-quotes.
- Part (c): In Maple, what is the value of y if
> a := 2; b := 2: y := 'a+b' + 2; # Those are right-quotes.
- Problem 7:
- In Maple, what is the output of the following two commands?
> x := [ 1, [2, 3, 4], [5, [6,7]], 8, [9]]:
> op(2, op(3,x));
- Problem 8:
- In Maple, what is the output for each of the following commands?
> nops( [1, 2, [3, [4, 5]], 6, [7]] );
> nops( x^2-3*x+2 );
- Problem 9:
- In Maple, what is the output of the following command? Briefly explain what the command is doing.
> op( 2, op( 2, x^2+2*x^3+z ) );
- Problem 10:
- In Maple, if x is a list, describe what the following command does, and how it does it.
> x := [ seq( op(i,x), i=2 .. nops(x) ), op(1,x) ];
- Problem 11:
- In Maple, what is the output of the following command?
> seq( seq( i+j, i=1..2), j=3..4);
- Problem 12:
- Let f be the mathematical function defined by
f(x,y) = (3y^2-5x)/(x+y).
- Part (a): How would you define f to Maple as a Maple expression named g?
- Part (b): How would you define f to Maple as a Maple function named h?
- Part (c): How would you define f to Maple as a Maple procedure named k?
- Problem 13:
- Draw the expression tree for the Maple expression
(x+y)/(3*y^2-5*x). What is
op(2,op(1,op(1,op(2,(x+y)/(3*y^2-5*x)))))?
- Problem 14:
- The following substitution command in Maple does not produce the same result that a substitution in an algebra or calculus class would produce. What result does the Maple command produce and why?
> subs( x+y = 5*z, x+y+5*z*sin(x+y)*(x+y)^(-2) );
- Problem 15:
- Compare the following two Maple procedures.
> f := proc( x::numeric )
> if x < 0 then
> 0
> else
> x
> fi
> end;
and
> g := proc( x::numeric )
> if x < 0 then
> if x > 0 then 0 fi
> else
> x
> fi
> end;
- Problem 16:
- The following conditional statement can be simplified. Try to simplify it as much as possible. (Hint: You don't need nested conditional statements here.)
> if x < 0 then
> -x^2
> else
> if x >= 0 then
> x^2
> fi
> fi
- Problem 17:
- What is the output from each of the following for-loops?
- Part (a):
> for i from -9 to 9 by 2 do i od;
- Part (b):
> for counter from 100 to 400 do
> if frac(sqrt(counter)) = 0 then
> print(counter, sqrt(counter))
> fi
> od;
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