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set xrange [-1:3]
set yrange [-2:10]
set key off
set xtics 0
set ytics 0
set border 0 0
set xzeroaxis
set yzeroaxis
set termoption dash
set xtics axis out ("" -0.5, "0.5" 0.5, "" 1, "" 1.5, "" 2, "" 2.5)
set ytics axis out ("" -1, "1.25" 1.25, "" 3, "" 5, "" 7, "" 9)
#set label 1 " n = 0 " at 2.35, 1.6, 0
set label 2 " n = 1 " at 1.9, 7, 0
set label 3 " n = 2 " at 1.6, 9.6, 0
set label 4 " n = 3 " at 2.7, 7.2, 0
set label 5 " 5x^2 - x^4 " at 1.5,3,0
set style line 1 lt 3 lw 1 pt 3 linecolor rgb "#1FBED6"
set style line 2 lt 1 lw 1 pt 1 linecolor rgb "#FF717E"
set style line 3 lt 3 lw 1 pt 2 linecolor rgb "#555555"
set style line 4 lt 1 lw 2 pt 4 linecolor rgb "#97C30A"
show label
set title "1st Four Terms of the Taylor Series Expansion of $f(x) = 5x^{2} - x^{4}$"
show title
set terminal svg
set output 'TaylorSeries.svg'
set arrow from 0.5, graph 0 to 0.5, graph 1 ls 1 nohead
plot 5*x**2 - x**4 ls 4, \
1.25 ls 1, \
5*0.5**2-0.5**4+(x-0.5)*(10*0.5-4*0.5**3) ls 2, \
5*0.5**2-0.5**4+(x-0.5)*(10*0.5-4*0.5**3)+(((x-0.5)**2)/2)*(10-12*0.5**2) ls 2, \
5*0.5**2-0.5**4+(x-0.5)*(10*0.5-4*0.5**3)+(((x-0.5)**2)/2)*(10-12*0.5**2)+(((x-0.5)**3)/6)*(0-24*0.5) ls 2