Problem # 1 Four points on the graph of f(x) = ln(x) are given: (1, 0), (3, 1.099), (6, 1.792), and (10, 2.303). a) Find a cubic polynomial g(x) which approximates the inverse function of f(x) by fitting the cubic g(x) to the points (0, 1), (1.099, 3), (1.792, 6), (2.303, 10). b) As you may know, the inverse function of In(x) is exp(x). Compose the values of g(x) and In(x) at the given values of x = 0.1, 1, 1.1, 2, 2.3, 3 and 4. c) Plot the graphs of g(x) and exp(x) in the same window for -1

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
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Problem 1 using maple lab plz
Problem # 1
Four points on the graph of f (x) = ln(x) are given: (1, 0), (3, 1.099), (6, 1.792), and (10, 2.303).
a) Find a cubic polynomial g(x) which approximates the inverse function of f(x) by fitting the cubic g(x) to
the points (0, 1), (1.099, 3), (1.792, 6), (2.303, 10).
b) As you may know, the inverse function of In(x) is exp(x). Compose the values of g(x) and In(x) at the
given values of x = 0.1, 1, 1.1, 2, 2.3, 3 and 4.
c) Plot the graphs of g(x) and exp(x) in the same window for -1 <x< 3. Why are the graphs close to
each other for some values of x but not for others?
d) Plot g(x) along with the following points in the same Cartesian Plane: (0, 1), (1.099, 3), (1.792, 6),
(2.303, 10).
Problem # 2
Define h(x) =
dt
a) Evaluate h(x) for x = 2, 4, 6, 8, 10. Plot the five points on h(x) which are determined by these five
values of x.
b) Display plots of h(x) and In(x) in the same window for 1 <xS 11.
Transcribed Image Text:Problem # 1 Four points on the graph of f (x) = ln(x) are given: (1, 0), (3, 1.099), (6, 1.792), and (10, 2.303). a) Find a cubic polynomial g(x) which approximates the inverse function of f(x) by fitting the cubic g(x) to the points (0, 1), (1.099, 3), (1.792, 6), (2.303, 10). b) As you may know, the inverse function of In(x) is exp(x). Compose the values of g(x) and In(x) at the given values of x = 0.1, 1, 1.1, 2, 2.3, 3 and 4. c) Plot the graphs of g(x) and exp(x) in the same window for -1 <x< 3. Why are the graphs close to each other for some values of x but not for others? d) Plot g(x) along with the following points in the same Cartesian Plane: (0, 1), (1.099, 3), (1.792, 6), (2.303, 10). Problem # 2 Define h(x) = dt a) Evaluate h(x) for x = 2, 4, 6, 8, 10. Plot the five points on h(x) which are determined by these five values of x. b) Display plots of h(x) and In(x) in the same window for 1 <xS 11.
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