lSum Practice with srange() -- Sage

f(x)=x^2 a = 0 b = 5 n = 10 h = (b-a)/n

srange(b)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left[0, 1, 2, 3, 4\right]$

srange(a,b)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left[0, 1, 2, 3, 4\right]$

srange(a,b,h)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left[0, \frac{1}{2}, 1, \frac{3}{2}, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}\right]$

[f(x) for x in srange(a,b,h)]

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left[0, \frac{1}{4}, 1, \frac{9}{4}, 4, \frac{25}{4}, 9, \frac{49}{4}, 16, \frac{81}{4}\right]$

[h*f(x) for x in srange(a,b,h)]

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left[0, \frac{1}{8}, \frac{1}{2}, \frac{9}{8}, 2, \frac{25}{8}, \frac{9}{2}, \frac{49}{8}, 8, \frac{81}{8}\right]$

sum([h*f(x) for x in srange(a,b,h)])

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{285}{8}$

sum([h*f(x) for x in srange(a,b,h)]).n()

 $\newcommand{\Bold}[1]{\mathbf{#1}}35.6250000000000$

def lSum(a,b,n,f): h=(b-a)/n return sum([h*f(x) for x in srange(a,b,h)]).n() f="x**2" show(lSum(0,5,10,lambda x: eval(f))) print "n\tlSum" for n in range(5): print "10^",n,"\t",lSum(0,5,10^n,lambda x: eval(f))

 $\newcommand{\Bold}[1]{\mathbf{#1}}35.6250000000000$ 
n	lSum
10^ 0 	0.000000000000000
10^ 1 	35.6250000000000
10^ 2 	41.0437500000000
10^ 3 	41.6041875000000
10^ 4 	41.6604168750000

n	lSum
10^ 0 	0.000000000000000
10^ 1 	35.6250000000000
10^ 2 	41.0437500000000
10^ 3 	41.6041875000000
10^ 4 	41.6604168750000

lSum Practice with srange()

2777 days ago by MATH4H2012