.MCAD 304020000 1 74 93 0
.CMD PLOTFORMAT
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 21 15 0 0 3 
.CMD FORMAT  rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=0
.CMD SET ORIGIN 0
.CMD SET TOL 0.001000000000000
.CMD SET PRNCOLWIDTH 8
.CMD SET PRNPRECISION 4
.CMD PRINT_SETUP 1.200000 0.979167 1.200000 1.200000 0
.CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty*
.CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFAULT_TEXT_PARPROPS 0 0 0
.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables
.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants
.CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text
.CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1
.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2
.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3
.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4
.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5
.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6
.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7
.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=2 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD UNITS U=1
.CMD DIMENSIONS_ANALYSIS 0 0
.CMD COLORTAB_ENTRY 0 0 0
.CMD COLORTAB_ENTRY 128 0 0
.CMD COLORTAB_ENTRY 0 128 0
.CMD COLORTAB_ENTRY 128 128 0
.CMD COLORTAB_ENTRY 0 0 128
.CMD COLORTAB_ENTRY 128 0 128
.CMD COLORTAB_ENTRY 0 128 128
.CMD COLORTAB_ENTRY 128 128 128
.CMD COLORTAB_ENTRY 192 192 192
.CMD COLORTAB_ENTRY 255 0 0
.CMD COLORTAB_ENTRY 0 255 0
.CMD COLORTAB_ENTRY 255 255 0
.CMD COLORTAB_ENTRY 0 0 255
.CMD COLORTAB_ENTRY 255 0 255
.CMD COLORTAB_ENTRY 0 255 255
.CMD COLORTAB_ENTRY 255 255 255
.TXT 5 7 1 0 0
Cg a67.000000,67.000000,25
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\fs32 MathCad Session 
in MAT200}}
.EQN 4 30 12 0 0
{0:a}NAME:3
.TXT 1 -30 8 0 0
Cg a67.000000,67.000000,60
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Defining a constant\par 
and evaluating expressions\par containing it}
.EQN 2 30 13 0 0
{0:a}NAME+1={0}?_n_u_l_l_
.EQN 3 0 14 0 0
({0:a}NAME)^(2)={0}?_n_u_l_l_
.TXT 4 -30 11 0 0
Cg a67.000000,67.000000,54
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Create formulas with the 
constant a\par and the variable x}
.EQN 1 30 18 0 0
(({0:a}NAME)^(3)+({0:a}NAME)^(2))/(({0:a}NAME)^(2)+3)={0}?_n_u_l_l_
.EQN 6 0 16 0 0
(({0:x}NAME)^(2)+{0:a}NAME)/(({0:x}NAME)^(2)+3){63}1
.TXT 5 -30 19 0 0
Cg a67.000000,67.000000,19
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Define functions...}
.EQN 1 29 20 0 0
{0:f}NAME({0:x}NAME):({0:x}NAME)^(2)-2
.EQN 3 0 21 0 0
{0:g}NAME({0:x}NAME):\({0:ln}NAME({0:x}NAME))
.TXT 4 -24 22 0 0
Cg a62.000000,62.000000,27
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard ... and evaluating them ...}
.EQN 0 24 23 0 0
{0:f}NAME(2)={0}?_n_u_l_l_
.EQN 3 0 25 0 0
{0:g}NAME(7)={0}?_n_u_l_l_
.TXT 5 -29 26 0 0
Cg a67.000000,67.000000,25
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Defining a range variable}
.EQN 0 28 27 0 0
{0:t}NAME:0.1,0.2;2
.TXT 4 -28 28 0 0
Cg a67.000000,67.000000,6
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Tables}
.EQN 0 22 29 0 0
{0:t}NAME=
.EQN 0 4 30 0 0
{0:f}NAME({0:t}NAME)=
.EQN 0 6 31 0 0
{0:g}NAME({0:t}NAME)=
.TXT 52 -25 32 0 0
Cg a60.000000,60.000000,39
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard and graphing, using the 
\par range variable}
.EQN 1 11 34 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:f}NAME({0:t}NAME),{0:g}NAME({0:t}NAME)@2&0&(_n_u_l_l_&_n_u_l_l_)&{0:t}NAME
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 2 2 NO-TRACE-STRING
0 1 1 0 2 2 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 2 36 38 10 0 3 
.TXT 49 -10 35 0 0
Cg a59.000000,59.000000,47
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard How the accuracy depends 
\par on the range variable}
.EQN 0 24 39 0 0
{0:t}NAME:0.1,0.5;2
.EQN 5 -13 38 0 0
1&-2&(_n_u_l_l_&_n_u_l_l_)&{0:f}NAME({0:t}NAME),{0:g}NAME({0:t}NAME)@2&0&(_n_u_l_l_&_n_u_l_l_)&{0:t}NAME
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 2 2 NO-TRACE-STRING
0 1 1 0 2 2 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 2 34 24 10 0 3 
.TXT 36 -14 40 0 0
Cg a62.000000,62.000000,58
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\fs28 Derivatives} with
\par variables, constants,\par and range variables}
.EQN 0 19 41 0 0
{0:x}NAME"{0:f}NAME({0:x}NAME){63}2*{0:x}NAME
.EQN 0 19 42 0 0
{0:a}NAME"{0:f}NAME({0:a}NAME)={0}?_n_u_l_l_
.TXT 0 10 44 0 0
Cg a14.000000,14.000000,28
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard this latter\par stands 
for\par f'(a)}
.TXT 5 -30 45 0 0
Cg a44.000000,44.000000,24
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard symbolic differentiation}
.EQN 6 1 51 0 0
{0:t}NAME"{0:f}NAME({0:t}NAME)=
.TXT 23 -18 52 0 0
Cg a61.000000,61.000000,51
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Next we define h to be 
the derivative function of g}
.EQN 4 15 48 0 0
{0:h}NAME({0:x}NAME):{0:x}NAME"{0:g}NAME({0:x}NAME)
.EQN 0 18 49 0 0
{0:h}NAME(1.1)={0}?_n_u_l_l_
.EQN 0 15 57 0 0
{0:h}NAME(3)={0}?_n_u_l_l_
.EQN 4 -15 53 0 0
{0:h}NAME(1.5)={0}?_n_u_l_l_
.TXT 5 -33 54 0 0
Cg a61.000000,61.000000,61
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard We graph g and its 
derivative h\par in the same coordinate system}
.EQN 0 31 55 0 0
{0:t}NAME:1.1,1.2;3
.EQN 6 -14 60 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:g}NAME({0:t}NAME),{0:h}NAME({0:t}NAME)@3&1.1&(_n_u_l_l_&_n_u_l_l_)&{0:t}NAME
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 2 2 NO-TRACE-STRING
0 1 1 0 2 2 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 31 34 10 0 3 
.EQN 1 -14 58 0 0
{0:t}NAME=
.EQN 0 6 59 0 0
{0:h}NAME({0:t}NAME)=
.TXT 47 9 61 0 0
Cg a43.000000,43.000000,78
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard what is the formula for 
h(x)=g'(x)? We use again the\par symbolic evaluation arrow}
.EQN 7 0 65 0 0
{0:x}NAME"{0:g}NAME({0:x}NAME){63}(1)/((2*(\({0:ln}NAME({0:x}NAME))*{0:x}NAME)))
.TXT 7 0 66 0 0
Cg a43.000000,43.000000,35
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard What is the second 
derivative of g?}
.EQN 6 0 67 0 0
((2,{0:x}NAME,{0:g}NAME({0:x}NAME)){62}){63}(-1)/((4*(({0:ln}NAME({0:x}NAME))^(((3)/(2)))*({0:x}NAME)^(2))))-(1)/((2*(\({0:ln}NAME({0:x}NAME))*({0:x}NAME)^(2))))
.TXT 9 0 70 0 0
Cg a43.000000,43.000000,17
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard Third derivative?}
.EQN 5 -8 72 0 0
((3,{0:x}NAME,{0:g}NAME({0:x}NAME)){62}){63}(3)/((8*(({0:ln}NAME({0:x}NAME))^(((5)/(2)))*({0:x}NAME)^(3))))+(3)/((4*(({0:ln}NAME({0:x}NAME))^(((3)/(2)))*({0:x}NAME)^(3))))+(1)/((\({0:ln}NAME({0:x}NAME))*({0:x}NAME)^(3)))
.TXT 12 -12 73 0 0
Cg a63.000000,63.000000,28
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard {\fs28 Integration:\par }
Antiderivatives}
.EQN 0 15 74 0 0
(({0:x}NAME,{0:f}NAME({0:x}NAME)){67}){63}(1)/(3)*({0:x}NAME)^(3)-2*{0:x}NAME
.EQN 7 0 75 0 0
(({0:x}NAME,{0:h}NAME({0:x}NAME)){67}){63}(({0:x}NAME,{0:h}NAME({0:x}NAME)){67})
.TXT 1 25 80 0 0
Cg a23.000000,23.000000,44
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard doesn't work like this,
\par but try the next ...}
.EQN 7 -25 76 0 0
(({0:x}NAME,(1)/(2*\({0:ln}NAME({0:x}NAME))*{0:x}NAME)){67}){63}\({0:ln}NAME({0:x}NAME))
.EQN 8 0 79 0 0
(({0:x}NAME,{0:x}NAME*({0:e}NAME)^({0:x}NAME)){67}){63}{0:x}NAME*{0:exp}NAME({0:x}NAME)-{0:exp}NAME({0:x}NAME)
.EQN 7 0 83 0 0
(({0:x}NAME,({0:x}NAME)^(2)*({0:e}NAME)^({0:x}NAME)){67}){63}({0:x}NAME)^(2)*{0:exp}NAME({0:x}NAME)-2*{0:x}NAME*{0:exp}NAME({0:x}NAME)+2*{0:exp}NAME({0:x}NAME)
.EQN 7 0 82 0 0
(({0:x}NAME,{0:ln}NAME({0:x}NAME)){67}){63}{0:x}NAME*{0:ln}NAME({0:x}NAME)-{0:x}NAME
.TXT 11 -16 84 0 0
Cg a64.000000,64.000000,18
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}\plain\cf1\fs20 \pard What about {\fs28 Limits}?}
.EQN 0 19 87 0 0
((3,{0:x}NAME,({0:x}NAME-3)/({0:x}NAME+2)){68}){63}0
.EQN 7 0 91 0 0
((-2,{0:x}NAME,({0:x}NAME-3)/({0:x}NAME+2)){68}){63}{0:undefined}NAME
.EQN 8 0 93 0 0
((4,{0:x}NAME,(\({0:x}NAME)-2)/({0:x}NAME-4)){68}){63}(1)/(4)