f = function(t){ 
  t/10 - cos(t)/5 + 1/5 - log(2) 
  }
ts = seq( 0, 10, length.out=100 )
y = f(ts)
plot( ts, y, type='l' )
grid()


library(stats)
res = uniroot( f, c(2.25, 3.5) )
res

10*log(2) 

f = function(t){ 
  t/10 - cos(t)/(10*pi) + 1/(10*pi) - log(2) 
  }
ts = seq( 0, 10, length.out=100 )
y = f(ts)
plot( ts, y, type='l' )
grid()

library(stats)
res = uniroot( f, c(6, 8) )
res

# Part d:
#
#postscript("../../WriteUp/Graphics/Chapter2/chap_2_sect_3_prob_14_plot.eps", onefile=FALSE, horizontal=FALSE)

y0 = 1
t = seq( 0, 8, length.out=500 )
ya = y0 * exp( t/10 - cos(t)/5 + 1/5 )
yb = y0 * exp( t/10 )
yc = y0 * exp( t/10 - cos(t)/(10*pi) + 1/(10*pi) )
plot( t, ya, col='blue', type='l', xlab='t', main='Problem 14' )
lines( t, yb, type='l', col='green' )
lines( t, yc, type='l', col='red' )
abline(h=2, col='black')
legend( 'topleft', c('Part (a)', 'Part (b)', 'Part (c)'), lwd=2, lty=rep(1, 3), col=c( 'blue', 'green', 'red' ) )
grid()
 
#dev.off()