Calculus 2 - Mathematics 120 - Spring 2008

These questions are for you to become aware of some important differences (and similiarites) between Excel, Mathematica, and "standard" mathematical conventions.

1. Does equal 2^(3^4) or (2^3)^4? The answer depends on whom you ask. If you ask a mathematician, it's 2^(3^4). If you "ask" Excel or Mathematica or your calculator, you may get different answers.
   Type 2^3^4, without any parentheses, into both Excel and Mathematica, to determine whether each of them interprets it as 2^(3^4) or (2^3)^4. Then record your answers in the following table. Fill out the rest of the table too.
   
   

   	Mathematics	Excel	Mathematica
   2^3^4	2^(3^4)
   2 + 3 * 4
   2 * 3 ^ 4
   2 * 3 / 4
   2 / 3 * 4
   2 * - 3
   2 + -3
   2 - + 3
   2 - * 3

   
   

2. How do we compute cos(2) in Excel or Mathematica?
   In Excel, you must use parentheses, but in Mathematica square brackets:
   Excel: =COS(2)  (If you don't capitalize, Excel will do it for you! But don't forget the equal sign.)
   Mathematica: Cos[2]  (the C must be uppercase, the os must be lowercase; otherwise Mathematica won't understand).
   
   Is the 2 interpreted as radians or degrees in each software? How do you know? Explain.
   
   
   
   
   
3. In Mathematica, type in 2(5). Do you get 10?
   
   Now do it in Excel: what does =2(5) give?
   
   
4. In Mathematica, type in 2*5. Do you get 10?
   
   Now do it in Excel: what does =2*5 give?
   
   
5. Try the following, in both Excel and Mathematica. (In Excel, prefix each with an equal sign.)
   
   2*(5+7)  vs.  2*[5+7]
   Cos(2)  vs.  Cos[2]
   
   What did you get with each software?
   
   
   
   
   
6. Fill out the following table. 
   Advice: It is often a good idea to use "unnecessary" but appropriatley placed spaces and  brackets for "easier human readability"!
   For example, x*y/z  and  (x*y)/z  and  x*y / z  all produce the same result; but the latter two are easier to read.
   

   How do you write	in Excel?	in Mathematica?
   cos x
   cos(x + y)
   cos(xy)
   cos xy
   cos x y
   cos x + y