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1$\"3Sbbb:85yFF17$$\"35LLL.a#o$GF1$\"3CbbbNp@\"*GF17$$\"3ammm^Q40IF1$
\"3)3666!fR.IF17$$\"3z******z]rfJF1$\"3')******>nZ1JF17$$\"3gmmmc%GpL$
F1$\"31666r*=YA$F17$$\"3/LLL8-V&\\$F1$\"3S))))))3oGILF17$$\"3=+++XhUkO
F1$\"3;LLLj2&HW$F17$$\"3=+++:o<EQF1$\"3:LLLVXy]NF17$$\"\"%F*$\"3^mmmmm
mmOF1-F^^m6&F`^m$F*F*Fj]n$\"*++++\"!\")-%+AXESLABELSG6$%\"xG%\"yG-%%VI
EWG6$;F(Fd]n%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 259 "" 0 "" {TEXT 
-1 0 "" }}{PARA 258 "" 0 "" {TEXT 258 18 "Problem 4 solution" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "sumofpr
imes:=k->sum(ithprime(i),i=1..k);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%,sumofprimesGR6#%\"kG6\"6$%)operatorG%&arrowGF(-%$sumG6$-%)ithprimeG6
#%\"iG/F2;\"\"\"9$F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 
"sumofprimes(5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#G" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 66 "We can just try to guess the answer, but \+
a nice way to solve this " }}{PARA 0 "" 0 "" {TEXT -1 35 "problem is a
 little 'while-do' loop" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "j:=1:\nw
hile sumofprimes(j)<=90000 do\nj:=j+1\nod:\nj-1;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"$\"=" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Answer: \+
k=181" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "sumofprimes(j);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"&j2*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "sumofprimes(j-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
\"&s'*)" }}}{EXCHG {PARA 267 "" 0 "" {TEXT -1 0 "" }}{PARA 261 "" 0 "
" {TEXT -1 1 "P" }{TEXT 260 18 "roblem 5 solutions" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 35 "approx_exp:=x->sum(x^n/n!, n=0..5);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%+approx_expGR6#%\"xG6\"6$%)operatorG%&arrowGF(-%
$sumG6$*&)9$%\"nG\"\"\"-%*factorialG6#F2!\"\"/F2;\"\"!\"\"&F(F(F(" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "(verify correctness of the formula
)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "approx_exp(1.0);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#$\"+nmm;F!\"*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "exp(-20.0); approx_exp(-20.0);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+AO:h?!#=" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+LLB:
@!\"&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "The error term for the a
pproximation above is given by" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 29 "error_term:=x->x^6*exp(x)/6!;" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%+error_termGR6#%\"xG6\"6$%)operatorG%&arrowGF(,$*&)9$\"\"'\"\"\"-
%$expG6#F/F1#F1\"$?(F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "To \+
find the interval where the accuracy is within .001 evaluate" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "fsolve (x^6*exp(x)/6!=.001);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+#=z3D)!#5" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 75 "Answer: accuracy is within .001 on the interval (-
.8250879182, .8250879182)" }}}{EXCHG {PARA 268 "" 0 "" {TEXT -1 0 "" }
}{PARA 262 "" 0 "" {TEXT -1 18 "Problem 6 Solution" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 19 "h:=x->(1+x)*exp(x);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"hGR6#%\"xG6\"6$%)operatorG%&arrowGF(*&,&\"\"\"F.9$F.F.-%$exp
G6#F/F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "`h(0)`=h(0
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%%h(0)G\"\"\"" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 13 "diff(h(x),x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&-%$expG6#%\"xG\"\"\"*&,&F(F(F'F(F(F$F(F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "subs(x=0,%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$-%$expG6#\"\"!\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "DDF:=diff(h(x),x,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%$DDFG,&-%$expG6#%\"xG\"\"#*&,&\"\"\"F-F)F-F-F&F-F-" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "DDF-h(x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$-%$expG6#%\"xG\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 75 "note: if you are using Maple 6 or  7, this problem doesn't make
 much sense," }}{PARA 0 "" 0 "" {TEXT -1 80 "since the return is exact
ly what you expect. If you are using an earlier version" }}{PARA 0 "" 
0 "" {TEXT -1 54 "of Maple, your answer will contain sinh(x) and cosh(
x)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "dsolve(\{diff(y(x),x,x)-y(x)=
2*exp(x),y(0)=1, D(y)(0)=2\},y(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#/-%\"yG6#%\"xG,&-%$expGF&\"\"\"*&F'F+F)F+F+" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 6 "eq:=%;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/
-%\"yG6#%\"xG,&-%$expGF(\"\"\"*&F)F-F+F-F-" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 11 "f:=rhs(eq);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"
fG,&-%$expG6#%\"xG\"\"\"*&F)F*F&F*F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "19 2 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 
1 1 }{PAGENUMBERS 0 1 2 33 1 1 }