date
 unsetenv DISPLAY
 cd ~/Symbolic/Maple/
 maple
pollux: pollux: Sun Nov 12 18:54:34 EST 1995
pollux: pollux: {{Maple}}     |\^/|     Maple V Release 3 (University of Florida)
._|\|   |/|_. Copyright (c) 1981-1994 by Waterloo Maple Software and the
 \  MAPLE  /  University of Waterloo. All rights reserved. Maple and Maple V
 <____ ____>  are registered trademarks of Waterloo Maple Software.
      |       Type ? for help.
                                     20872

# Part a of the first problem on TakeHome B.

> y := (1/2)*(exp(x) + exp(-x)) ;


                         y := 1/2 exp(x) + 1/2 exp(- x)



# I use dydx to mean the derivative dy/dx

> dydx := diff(y,x) ;

                       dydx := 1/2 exp(x) - 1/2 exp(- x)

> 1 + dydx^2 ;

                                                       2
                        1 + (1/2 exp(x) - 1/2 exp(- x))



# We now compute ds/dx, the infinitesimal arclength .

> dsdx := simplify(  sqrt(1 + dydx^2 ) ) ;

                                                           1/2
                  dsdx := 1/2 (2 + exp(2 x) + exp(- 2 x))


# Now we integrate 

> int(2*Pi*y*dsdx, x =0..1) ;

                                        2             4

                            Pi (4 exp(1)  - 1 + exp(1) )
                        1/4 ----------------------------
                                             2
                                       exp(1)


# The quote symbol, " ,below means `the value resulting from the previous calculation'.

> ans  := " ;

                                           2             4
                               Pi (4 exp(1)  - 1 + exp(1) )
                    ans := 1/4 ----------------------------
                                                2
                                          exp(1)



> ans1 := simplify(") ;

                 ans1 := 1/4 Pi (4 exp(2) - 1 + exp(4)) exp(-2)


> expand(ans1) ;

           Pi exp(-2) exp(2) - 1/4 Pi exp(-2) + 1/4 Pi exp(-2) exp(4)

> simplify(") ;

                      Pi - 1/4 Pi exp(-2) + 1/4 Pi exp(2)

> parta_surfacearea = " ;

          parta_surfacearea = Pi - 1/4 Pi exp(-2) + 1/4 Pi exp(2)