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# Scientific Programming Assignment 3

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CSc 30100 – Scientific Programming

Assignment

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0
Calculate the Taylor polynomials centered at 0,
0 , !
for cos for the following 4 values of ,
1234 , , , which is equivalent to 10 10 10 10
, for 1,2,3,4. 10
For each value of ,
k n
k
n
k
f T x x
k
f x x
x
j x j
j
=
=
=
 
∈   
= =

12
find the smallest integer such that
cos 10 .
10 10 n
n
j j T   −
  − <  
2
.
3
Calculate the “exact” value using np.cos(x). Present your results
in a table and discuss them. How do your errors compare to the
error bounds for Taylor polynomials that we discussed in class?
Rememb
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1
1
er that the error for a Taylor polynomial is given by its
remainder term
=
1 !
Include all of your analysis and discussion in an .ipynb file
and submit the file through Blackbo
n
n
n n
f c R x fx T x x a
n
+
+
= − − +
ard. The name of the
file you submit should be lastname_firstname_AS03.ipynb.
Do not clear your results after your last run so that I will be Scientific Programming Assignment 3