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{SECT 0 {PARA 256 "" 0 "" {TEXT 256 23 "Laboratory Exercise 2.4" }
{TEXT 257 35 "\nTangent Lines and Rates of Change\n" }{TEXT 258 14 "(C
CH Text 2.2)" }{MPLTEXT 1 0 2 "\n\n" }}{SECT 1 {PARA 3 "" 0 "" {TEXT 
-1 19 "The function is ..." }}{PARA 0 "" 0 "" {TEXT -1 4 "Let " }
{XPPEDIT 18 0 "f(x) = 3x-2x^2" "/-%\"fG6#%\"xG,&*&\"\"$\"\"\"F&F*F**&
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{TEXT -1 9 "Problem 1" }}{PARA 0 "" 0 "" {TEXT -1 87 "One good way to \+
do this would be by by hand using the limit of the difference quotient
:" }}{PARA 0 "" 0 "" {XPPEDIT 18 0 "limit( (f(0.5+h)-f(0.5))/h,h=0);" 
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\"\"F.F/F5/F/\"\"!" }{TEXT -1 80 "\nHowever, the worked example on pag
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{MPLTEXT 1 0 16 "f:=x->3*x-2*x^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
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{TEXT -1 37 "\nThe instantaneous rate of change of " }{XPPEDIT 18 0 "f
" "I\"fG6\"" }{TEXT -1 4 " at " }{XPPEDIT 18 0 "x=0.5" "/%\"xG$\"\"&!
\"\"" }{TEXT -1 56 " is 1.  That is, for every unit we move in the\npo
sitive " }{XPPEDIT 18 0 "x" "I\"xG6\"" }{TEXT -1 41 " direction we wil
l go up one unit in the " }{XPPEDIT 18 0 "y" "I\"yG6\"" }{TEXT -1 12 "
 direction. " }{MPLTEXT 1 0 1 "\n" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 
-1 9 "Problem 2" }}{PARA 3 "" 0 "" {TEXT 265 65 "Since we have the slo
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" {XPPMATH 20 "6#$\"$+\"!\"#" }}{PARA 0 "" 0 "" {TEXT -1 27 "\nThe lin
e has the equation " }{XPPEDIT 18 0 "y-1=1(x-0.5)" "/,&%\"yG\"\"\"\"\"
\"!\"\"-\"\"\"6#,&%\"xGF%$\"\"&!\"\"F'" }{TEXT -1 4 " or " }{XPPEDIT 
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\"\"!7$$!1LLLe%G?y%F*$\"1nmm\"p0k&>!#:7$$!1mmT&esBf%F*$\"1LL3<XZ=>F37$
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The graph above could be used to find the limit as h goes to zero by r
eading off the value at h=0.  Now it should\nbe pointed out that this \+
value does not exist, but the graph is only missing that one point so \+
we can make a very\ngood guess as to the value." }}}}{MARK "1" 0 }
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