1. Consider P(x) = -0.02x +0.1x2 – 0.2x + 1.66, which passes through the four points (1, 1.54), (2, 1.5), (3, 1.42), and (5, 0.66). (a) Find P(4). (b) Find P'(4). (c) Find the definite integral of P(x) taken over [1, 4].
1. Consider P(x) = -0.02x +0.1x2 – 0.2x + 1.66, which passes through the four points (1, 1.54), (2, 1.5), (3, 1.42), and (5, 0.66). (a) Find P(4). (b) Find P'(4). (c) Find the definite integral of P(x) taken over [1, 4].
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.4: Derivatives Of Exponential Functions
Problem 26E: Find derivatives of the functions defined as follows. y=4-5x+2
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Transcribed Image Text:1. Use the fixed point iteration algorithm to approximate the fixed points (if any) of the
following functions to 12 decimal places. Produce a graph of each function and the line
y=x that clearly shows any fixed points.
(a) g(x)=x° – 3x – 2x² + 2
(b) g(x) = cos(sin(x))
(c) g(x) = x² – sin(x + 0.15)
(d) g(x)=x*-cos(x)
![Exercises for Introduction to Interpolation
1. Consider P(x) = -0.02x + 0.1x2 – 0.2x + 1.66, which passes through the four
points (1, 1.54), (2, 1.5), (3, 1.42), and (5, 0.66).
(a) Find P(4).
(b) Find P'(4).
(c) Find the definite integral of P(x) taken over [1, 4].
(d) Find the extrapolated value P(5.5).
(e) Show how to find the coefficients of P(x).
2. Consider P(x) = -0.04x +0.14x? – 0.16x +2.08, which passes through the four
points (0, 2.08), (1, 2.02), (2, 2.00), and (4, 1.12).
(a) Find P(3).
(b) Find P'(3).
(c) Find the definite integral of P(x) taken over (0, 3].
(d) Find the extrapolated value P(4.5).
(e) Show how to find the coefficients of P(x).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F306db5aa-6080-42dc-a25c-dcf7915ec897%2F4a246976-62fa-4b9b-93cb-d9db262aaff8%2Fn2wl2yo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercises for Introduction to Interpolation
1. Consider P(x) = -0.02x + 0.1x2 – 0.2x + 1.66, which passes through the four
points (1, 1.54), (2, 1.5), (3, 1.42), and (5, 0.66).
(a) Find P(4).
(b) Find P'(4).
(c) Find the definite integral of P(x) taken over [1, 4].
(d) Find the extrapolated value P(5.5).
(e) Show how to find the coefficients of P(x).
2. Consider P(x) = -0.04x +0.14x? – 0.16x +2.08, which passes through the four
points (0, 2.08), (1, 2.02), (2, 2.00), and (4, 1.12).
(a) Find P(3).
(b) Find P'(3).
(c) Find the definite integral of P(x) taken over (0, 3].
(d) Find the extrapolated value P(4.5).
(e) Show how to find the coefficients of P(x).
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