Near-infrared spectroscopy (NIRS) is an analytical method that uses electromagnetic spectrum from 780 nm to 2500 nm in various non-destructive measurement applications. The measured signal of five wavelengths are tabulated in the Table 1. To improve the quality of the NIRS signals, the rate of change can be computed to eliminate unwanted signals. Table 1 Wavelength, x (nm) Measured Signal, E(x) (unit) 750 900 950 1000 1150 12.34 87.23 332.12 455.74 429.41 By applying all appropriate numerical first order derivative methods to the following questions: (i) Estimate the rate of change of the signal when the wavelength was 950 nm using an interval of 50 nm. (ii) Estimate the rate of change of the signal when the wavelength was 950 nm using an interval of 200 nm. (iii) Identify the best method in estimating the rate of change of the signals with a concise justification if the exact solution is 2.4566.
Near-infrared spectroscopy (NIRS) is an analytical method that uses electromagnetic spectrum from 780 nm to 2500 nm in various non-destructive measurement applications. The measured signal of five wavelengths are tabulated in the Table 1. To improve the quality of the NIRS signals, the rate of change can be computed to eliminate unwanted signals. Table 1 Wavelength, x (nm) Measured Signal, E(x) (unit) 750 900 950 1000 1150 12.34 87.23 332.12 455.74 429.41 By applying all appropriate numerical first order derivative methods to the following questions: (i) Estimate the rate of change of the signal when the wavelength was 950 nm using an interval of 50 nm. (ii) Estimate the rate of change of the signal when the wavelength was 950 nm using an interval of 200 nm. (iii) Identify the best method in estimating the rate of change of the signals with a concise justification if the exact solution is 2.4566.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 45SE: A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the...
Related questions
Question
Numerical methods
using taylor's series
Transcribed Image Text:Near-infrared spectroscopy (NIRS) is an analytical method that uses electromagnetic spectrum from
780 nm to 2500 nm in various non-destructive measurement applications. The measured signal of five
wavelengths are tabulated in the Table 1. To improve the quality of the NIRS signals, the rate of
change can be computed to eliminate unwanted signals.
Table 1
Wavelength, x (nm)
Measured Signal, E(x) (unit)
750
900
950
1000
1150
12.34
87.23
332.12
455.74
429.41
By applying all appropriate numerical first order derivative methods to the following questions:
(i)
Estimate the rate of change of the signal when the wavelength was 950 nm using an interval
of 50 nm.
(ii)
Estimate the rate of change of the signal when the wavelength was 950 nm using an interval
of 200 nm.
(iii)
Identify the best method in estimating the rate of change of the signals with a concise
justification if the exact solution is 2.4566.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning