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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 15 "Basic Functions" }}
{PARA 257 "" 0 "" {TEXT -1 30 "and how to enter them in maple" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 74 "We shall \+
use the function syntax to define some important functions below." }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 257 57 "Polynomials, Rational functions, \+
Roots and Absolute Value" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "p := x -> x^4 - 3*x^2 +
6;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "r := x -> (x^2+1)/(3*
x + 5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "s := x -> sqrt(x
^2+1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "q := x -> root[4]
(x+2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "f := x -> abs(x^2
-3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Check :" }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 29 "f(x); p(x); q(x); r(x); s(x);" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT 258 36 "Exponential Functions and Logarithms" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "f := x -> exp(x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 6 "Check:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "g := x -> exp(-2*x+3);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "h := x -> 4^x - 3^(-x^2);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "r := x -> ln(x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "q := x -> log(x);" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 77 "Both, ln and log yield the natural logarithm, s
ince their difffrence is zero:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "r
(x)-q(x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "This is the common l
ogarithm, logs with other bases can be entered in a similar way." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "p := x -> log[10](x);p(10);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 259 24 "Trigonometric Functions:" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 17 "f := x -> sin(x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "g := x -> cos(2*x+1);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "h := x -> tan(Pi*x);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 5 "Check" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f(x); g(x); h(
x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Two ways of entering the f
unction   " }{XPPEDIT 18 0 "sin^2;" "6#*$%$sinG\"\"#" }{TEXT -1 3 " x \+
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f := x -> sin(x)^2;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "g := sin^2;" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 6 "Check:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f(x)-g(x
);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "The next two functions are \+
different:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "p := x -> sin(2*x)^2;
 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "q := x -> sin(2*x^2);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "A graph will tell the differe
nce" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "plot([p(x),q(x)],x=-1..4,col
or=[red,blue]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Inverse trig. \+
functions:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f := x -> arctan(x);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "g := x -> arcsin(2*x);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 1 }{VIEWOPTS 1 1 0 1 1 
1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }