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{SECT 0 {PARA 256 "" 0 "" {MPLTEXT 0 21 0 "" }}{PARA 257 "" 0 ""
{TEXT 256 14 "Calculus Lab 2" }}{PARA 3 "" 0 "" {TEXT -1 291 "An ant i
s walking over its ant mound whose height is given by a function h. On
the other side of the mound there is a blade of grass that the ant do
esn's see at the original location x=0. Now let the ant walk over the \+
mound and find the point at which the ant first sees the blade of gras
s. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 4 "" 0 "" {TEXT
-1 27 "The function h is given by " }{XPPEDIT 18 0 "h:=x->(x^2/16-2*x+
80)/(x^2/16-2*x+20)^2" ">%\"hG:6#%\"xG7\"6$%)operatorG%&arrowG6\"*&,(*
&F&\"\"#\"#;!\"\"\"\"\"*&\"\"#F2F&F2F1\"#!)F2F2*$,(*&F&\"\"#\"#;F1F2*&
\"\"#F2F&F2F1\"#?F2\"\"#F1F+F+" }}{PARA 4 "" 0 "" {TEXT -1 421 "Callin
g sequence for functions: f:=(x)->expression. Frame the formula of \+
h \nby clicking inside with the left mouse button; go to edit, click o
n `copy', go\nto the prompt, place the pointer at the prompt, go to ed
it, click on paste.\nNow the formula appears at the prompt. Click with
the right mouse button\nthere and select Maple input and deselect sta
ndard math; put semicolon at the end of the formula, and press enter:
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?" }}}}{SECT 0 {PARA 3 "
" 0 "" {TEXT -1 61 "The blade of grass is the vertical segment [[32,1/
5],[32,8]]." }}{PARA 3 "" 0 "" {TEXT -1 63 "Calling sequence: assign
`grass' to this segment. Plot grass." }}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 1 "?" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 59 "Plot the m
ound and grass together over the interval [0,32]:" }}{EXCHG {PARA 0 ">
" 0 "" {MPLTEXT 1 0 1 "?" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 51 "Wo
rk out the derivative of h at an arbitrary point." }}{PARA 0 "" 0 ""
{TEXT 257 29 "Calling sequence: D(function)" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 1 "?" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 59 "Write do
wn the equation of the tangent line at an arbitrary" }}{PARA 0 "" 0 "
" {TEXT 258 75 "point `a'. Assign `line', this is a function of two va
riables, `x' and `a'." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?" }
}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 130 "Determine `a' in floatig poin
t decimals from the condition that the line has height 8 at x=32. Call
ing sequence solve( lhs=rhs, a)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
1 0 1 "?" }}}}{PARA 3 "" 0 "" {TEXT -1 58 "Now download calculus_00.ms
and play the animated version." }}}{MARK "4 2 0 0" 1 }{VIEWOPTS 1 1
0 3 2 1804 }