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73 "b)  Plot `left endpoint rectangles' for x from 0 to 4 using 8 rect
angles." }}{PARA 0 "" 0 "" {TEXT -1 63 "c)  Have Maple calculate a `le
ftsum' for the above rectangles. " }}{PARA 0 "" 0 "" {TEXT -1 74 "d)  \+
Increase the number of rectangles to 16 and repeat parts (b) and (c). \+
" }}{PARA 0 "" 0 "" {TEXT -1 76 "e)  Increase the number of rectangles
 to 128  and repeat parts (b) and (c). " }}{PARA 0 "" 0 "" {TEXT -1 
86 "f)  What happens to the area of the rectangles as the number of re
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G6$Q\"x6\"Q!6\"-%%VIEWG6$;F(F\\`l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 
1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve \+
4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve
 11" "Curve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17
" "Curve 18" "Curve 19" "Curve 20" "Curve 21" "Curve 22" "Curve 23" "C
urve 24" "Curve 25" "Curve 26" "Curve 27" "Curve 28" "Curve 29" "Curve
 30" "Curve 31" "Curve 32" "Curve 33" "Curve 34" "Curve 35" "Curve 36
" "Curve 37" "Curve 38" "Curve 39" "Curve 40" "Curve 41" "Curve 42" "C
urve 43" "Curve 44" "Curve 45" "Curve 46" "Curve 47" "Curve 48" "Curve
 49" "Curve 50" "Curve 51" "Curve 52" "Curve 53" "Curve 54" "Curve 55
" "Curve 56" "Curve 57" "Curve 58" "Curve 59" "Curve 60" "Curve 61" "C
urve 62" "Curve 63" "Curve 64" "Curve 65" "Curve 66" "Curve 67" "Curve
 68" "Curve 69" "Curve 70" "Curve 71" "Curve 72" "Curve 73" "Curve 74
" "Curve 75" "Curve 76" "Curve 77" "Curve 78" "Curve 79" "Curve 80" "C
urve 81" "Curve 82" "Curve 83" "Curve 84" "Curve 85" "Curve 86" "Curve
 87" "Curve 88" "Curve 89" "Curve 90" "Curve 91" "Curve 92" "Curve 93
" "Curve 94" "Curve 95" "Curve 96" "Curve 97" "Curve 98" "Curve 99" "C
urve 100" "Curve 101" "Curve 102" "Curve 103" "Curve 104" "Curve 105" 
"Curve 106" "Curve 107" "Curve 108" "Curve 109" "Curve 110" "Curve 111
" "Curve 112" "Curve 113" "Curve 114" "Curve 115" "Curve 116" "Curve 1
17" "Curve 118" "Curve 119" "Curve 120" "Curve 121" "Curve 122" "Curve
 123" "Curve 124" "Curve 125" "Curve 126" "Curve 127" "Curve 128" "Cur
ve 129" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "leftsum(f(x), x \+
= 0..4, 128);" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%$S
umG6$,&*$)%\"iG\"\"#\"\"\"#F,\"%C5\"\"$F,/F*;\"\"!\"$F\"#F,\"#K" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }{TEXT -1 0 "" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Q%)R3L!\")" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 82 "As the number of rectangles increases, the total are
a of the rectangles limits to " }}{PARA 0 "" 0 "" {TEXT -1 40 "the are
a of the curve from x = 0 to 4.  " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "Int(f(x),x);" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%$IntG6$,&*$)%\"xG\"\"#\"\"\"F+\"\"$F+F)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "int(f(x),x);" }{TEXT -1 0 "" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"xG\"\"$\"\"\"#F(F'*&F'F(F&F(F(
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "int(f(x),x= 0..4);" }
{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"$+\"\"\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }{TEXT -1 0 "" }}
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"" {TEXT 257 9 "Example 2" }{TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT 
-1 21 "Let g ( x ) = x + 5. " }}{PARA 0 "" 0 "" {TEXT -1 40 "a)   Plot
  g ( x )  for x from 0 to 3.  " }}{PARA 0 "" 0 "" {TEXT -1 98 "b)  Us
ing triangles and rectangles, compute the area of the graph of  g ( x \+
)  for x from 0 to 3. " }}{PARA 0 "" 0 "" {TEXT -1 73 "c)  Plot `left \+
endpoint rectangles' for x from 0 to 3 using 3 rectangles." }}{PARA 0 
"" 0 "" {TEXT -1 63 "d)  Have Maple calculate a `leftsum' for the abov
e rectangles. " }}{PARA 0 "" 0 "" {TEXT -1 74 "e)  Increase the number
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