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{TEXT -1 80 "B.  Based on the inspection of DF describe how the soluti
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ving the directional field with the y-axi  extended to 100 and the t a
xis extended to 4e35, we can observe that the solution moves towards z
ero as t becomes larger and larger.  This is reinforced by finding the
 solution and limit of the solution as it goes towards infinity." }}
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45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "
Karen := dsolve(athena1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&KarenG
/-%\"yG6#%\"tG*&,(-%$sinGF(\"\"\"*&F)F.-%$cosGF(F.!\"\"%$_C1GF.F.*$)F)
\"\"#F.F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "limit(Karen, t
=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&limitG6$-%\"yG6#%\"
tG/F*%)infinityG\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 95 "C.  Fin
d the general solution and use it to determine its behaviour when t ap
proaches infinity." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 29 "     (See DE solution above.)" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 82 "     We can see that the soluti
on goes towards zero as t moves towards infinity.  " }}}}{MARK "8 4 0
" 82 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }