(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.
(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.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
Python coding. Do number (2)
![(1) Write a function which takes a list of the coefficients of a polynomial
P(x) = @o+ @l® +a+…+an n
of arbitrary degree n, and a value of xo, and returns P(xo). 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) = 5x² 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 5
n
n=1
x
2
OR
+
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) (a) Use your Horner's method function to evaluate the polynomial (x − 2)¹ 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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F986f6c25-9d5d-4e3f-93bc-35b073c4428b%2F0c8d075d-a487-4911-9446-4db256e0b191%2Fg63q2xf_processed.png&w=3840&q=75)
Transcribed Image Text:(1) Write a function which takes a list of the coefficients of a polynomial
P(x) = @o+ @l® +a+…+an n
of arbitrary degree n, and a value of xo, and returns P(xo). 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) = 5x² 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 5
n
n=1
x
2
OR
+
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) (a) Use your Horner's method function to evaluate the polynomial (x − 2)¹ 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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