,calculus ,a1 ,lab #1

  ,^! pro#ms >e aim$ pr9cip,y at
famili>iz+ y ) ,maple1 ?\< ,i al ?9k t
at l1/ "s ( !m mi<t help y 6le>n "s?+
use;l & b1uti;l4
  ,y probably ne$ 6"w 9 pairs1 r ?an 9
l>g] gr\ps4 ,pl1se take turns us+ !
keybo>d s t ea* p]son has a *.e 6get a
feel =! program4 ,/>t \ 0"w+ "? 5 ( my
,maple ov]view 6feel -=ta#1 !n answ] !
foll[+ "qs4 ,turn 9 a writeup on ,mon"d4
 
  #0_4 ,-pute #30 digits ( .p, #30
digits ( cos (37), & #30 digits (
sin (1.3 rad)_4
 
  #1_4 ,plot y .k x^4"-2x^2"+x_4 ,pick
ranges =! ;x & ;y axes t %[ z _m
important & 9t]e/+ f1tures (! func;n z
possi#4
 
  #2_4 ,d ! same ?+ )

                                      #j
  y .k x^3"+?1_/(x-1)^2"#-?150_/1+(x
    +3)^4"#_4
 
  #3_4 ,9 ! mid-#17? c5tury1 ,pi]re de
,f]mat 3jectur$ t = e
  n .k #0, #1, #2, ''' ! numb]
#2^(2^^n^)"+1 wd 2 prime4 (,a prime is a
:ole numb] hav+ no positive divisors
except xf & #1_4) ,he _h notic$1 = 9/.e1
t if n .k #0, !n
#2^(2^^0^)"+1 .k #2^1"+1 .k #3 is a
prime1 & t :5 n .k #1, !n
#2^(2^^1^)"+1 .k #2^2"+1 .k #5 is a
prime4
  ,r\<ly a c5tury lat]1 ,leon>d ,eul]
f9,y %[$ :e!r or n ,f]mat 0 "r4 (,bo? ^!
m5 7 ! grte/ ma!maticians ( _! "d_4) ,0
,f]mat "r8
 
  #4_4 ,d ! curves y .k x^4"-2x^2"+x &
y .k #10x-11 9t]sect8 ,if s1 ": & h[
(t54 ,if n1 :y n8
 

                                      #a
  #5_4 ,let f(x) .k x^3"-3x_4
  =(a) ,-p>e ! graphs ( f(x), f(x)+2,
f(x)-1_4 ,c y g5]alize yr obs]v,ns8 ,9
o!r ^ws1 c y f9d a rule = describ+ !
graph ( f(x)+k 9 t]ms (! graph ( f(x) :
wd "w = any func;n ;f & any 3/ant ;k_8
  =(;b) ,-p>e ! graphs ( f(x), f(x+2),
f(x-1)_4 ,c y g5]alize yr obs]v,ns8
  =(;c) ,-p>e ! graphs ( f(x), #3f(x),
f(x)_/2_4 ,c y g5]alize yr obs]v,ns8
  =(;d) ,-p>e ! graphs ( f(x), f(3x),
f(x_/2)_4 ,c y g5]alize yr obs]v,ns8












                                      #b