Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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![(1) Write a function which takes a list of the coefficients of a polynomial
P(x) = ao + a₁x + a² +
+anxn
of arbitrary degree n, and a value of xo, and returns P(x). You can use the function given in lectures,
ensuring you understand how it works.
(2) Use the function to evaluate
(a) P₁(x) = x³ + x² + 5x + 1 at x = 2.
(b) P₂(x) = 5 — x² at x = √3.
Are these answers exact? Explain why or why not.
(Use a print statements to show the evaluation of your function, and answer the question in a comment.)
(3) The Maclaurin series for the natural logarithm ln(1 + x) is given by
∞
ln(1 + x) = Σ(−1)¹+1
n=1
xn
n
= x -
2
X
x³
+
2 3
for all x. Use the first five terms in this series in the Horner evaluation function at a suitable value of x to give
an approximation of In 3/2.
4
(4) (a) Use your Horner's method function to evaluate the polynomial (x − 2)ª at the point x = = 2.0001.
(b) Is this answer correct?
(c) Give brief reasoning for this answer.
(5) In week 3 we wrote a function to convert from binary to decimal. The efficiency of this function can be
improved using the same principle as Horner's method. Write such a function (horner_ternary_to_dec)
using the ideas of Horner's method which takes a list containing Os, 1s and 2s (representing a base-3
number) and returns the corresponding decimal integer (so the input [1,2,0] returns the integer 15).](https://content.bartleby.com/qna-images/question/986f6c25-9d5d-4e3f-93bc-35b073c4428b/2ddd85ac-58b8-4db4-b6fe-35aa12cd3766/67oot5o_processed.png)
Transcribed Image Text:(1) Write a function which takes a list of the coefficients of a polynomial
P(x) = ao + a₁x + a² +
+anxn
of arbitrary degree n, and a value of xo, and returns P(x). You can use the function given in lectures,
ensuring you understand how it works.
(2) Use the function to evaluate
(a) P₁(x) = x³ + x² + 5x + 1 at x = 2.
(b) P₂(x) = 5 — x² at x = √3.
Are these answers exact? Explain why or why not.
(Use a print statements to show the evaluation of your function, and answer the question in a comment.)
(3) The Maclaurin series for the natural logarithm ln(1 + x) is given by
∞
ln(1 + x) = Σ(−1)¹+1
n=1
xn
n
= x -
2
X
x³
+
2 3
for all x. Use the first five terms in this series in the Horner evaluation function at a suitable value of x to give
an approximation of In 3/2.
4
(4) (a) Use your Horner's method function to evaluate the polynomial (x − 2)ª at the point x = = 2.0001.
(b) Is this answer correct?
(c) Give brief reasoning for this answer.
(5) In week 3 we wrote a function to convert from binary to decimal. The efficiency of this function can be
improved using the same principle as Horner's method. Write such a function (horner_ternary_to_dec)
using the ideas of Horner's method which takes a list containing Os, 1s and 2s (representing a base-3
number) and returns the corresponding decimal integer (so the input [1,2,0] returns the integer 15).
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