Two calculator exam problems

[dizzy]

The first one is easy:

Code:

\<<
  'F(X)'
  '1 + X*(2 - X*(3 - X*(4 - X*(1 + X))))'
  DUP UNROT = DEF
  F
  '1/2' -
  SOLVEVX
\>>

Which yields:

Quote:{X=0.213992196216 X=... }

Similarly:

Code:

\<<
'F(X)=SIN(1/X)' DEF
'SIN(1/X)' F F F
\>>

You could graph this or use try to optimize it somehow.