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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "ForClassA13_2.mws\nThu Oct
 13 12:59:07 MDT 2005\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "r
estart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "################
#########################" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }
{MPLTEXT 0 21 49 "# A #############################################" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "eq := x^2 - y^2 = 7^2 - 3^
2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f := x -> eq;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "f(1); f(2); f(3); f(4);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "############################
######" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "f := x -> x^2 - y
^2 = 7^2 - 3^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "f(1); f(
2); f(3); f(4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f := (x,
y) -> eq;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f(2,1);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f := unapply(eq, x,y);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f(1,2);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 4 "GIGO" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{MPLTEXT 0 21 49 "# B #############################################" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "#Graph of the white-board \+
function" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "f := x -> exp(-
3*x) -  arctan(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(0);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f(ln(2));  evalf(%);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(f, -10..10, -10..10);
" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 51 "# C ####################
###########################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 52 "f := x -> (1/4)*(x^3-3/2*x^2-6*x+2);  XRG :=
 -2..10;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "YRG := XRG;" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "fp := D(f);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "fp(0);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "fpp := D(fp);  (D@@2)(f);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 50 "plot([f,fp,fpp],XRG, YRG,colour=[black,red,blue]);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "fsolve( fp(x)=0, x=0..1
0);" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 65 "# D #################
############################################" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 46 "g := x -> (1+2/x)^x;   # For Positive x Values" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "plot(g, 0..5280);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "Maybe a horizontal asymptote:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "Limit( g(x), x=infinity);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "HA := value(%); evalf(HA);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot([g, HA], 0..50);" 
}}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 62 "# E ######################
####################################" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "f := x \+
-> (x^2 - 3)/x^3;  f(sqrt(3));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 26 "fp := D(f);  fpp := D(fp);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 56 "plot([f,fp,fpp], -4..4, -2..2, colour=[black,red,blue
]);" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 63 "# F #################
##########################################" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 18 "with(RealDomain); " }{TEXT -1 19 "MATH 147 & MATH 1
70" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "f := x -> 3/5*x^(5/3)
 - 3*x^(2/3): f(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "#fp \+
:= D(f);  fp(t);  " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "fpexp
 := diff( f(x), x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "fp :
= unapply(fpexp, x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "plo
t([f,fp]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "f(-1);  " }
{TEXT -1 23 "We expect f(-1) = -18/5" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
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