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Question 1 (a) A biologist who is studying the growth of a bacteria culture, recorded the following data 036 9 p(t) | 2 3 46 where p(t) denotes the number of bacteria at time t (minutes). Use natural cubic spline to estimate the number of bacteria at t = 5. (b) Consider the function Ax) = 1/(1+x²) (i) Construct the clamped cubic spline that interpolates the function at x = -2,-1,0,1 and 2. (ii) Compare the interpolated values with the true values at x = -1.5,-0.5,0.5, and 1.5 (c) Determine whether the following function is a cubic spline -x² + 1 if 0 < x s 1 (x-1)' +2(x- 1) if 1 < x < 2 | | 2х - 1 if 2 < x < 3

Question 1 (a) A biologist who is studying the growth of a bacteria culture, recorded the following data 036 9 p(t) | 2 3 46 where p(t) denotes the number of bacteria at time t (minutes). Use natural cubic spline to estimate the number of bacteria at t = 5. (b) Consider the function Ax) = 1/(1+x²) (i) Construct the clamped cubic spline that interpolates the function at x = -2,-1,0,1 and 2. (ii) Compare the interpolated values with the true values at x = -1.5,-0.5,0.5, and 1.5 (c) Determine whether the following function is a cubic spline -x² + 1 if 0 < x s 1 (x-1)' +2(x- 1) if 1 < x < 2 | | 2х - 1 if 2 < x < 3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 1 (a) A biologist who is studying the growth of a bacteria culture, recorded the following data 0369 p(t) 2 3 4 6 where p(t) denotes the number of bacteria at time t (minutes). Use natural cubic spline to estimate the number of bacteria at t = 5. (b) Consider the function Ax) = 1/(1+x²) (i) Construct the clamped cubic spline that interpolates the function at x = -2,-1,0,1 and 2. %3D (ii) Compare the interpolated values with the true values at x = -1.5,-0.5,0.5, and 1.5 (c) Determine whether the following function is a cubic spline -x² + 1 if 0 < x s 1 (x – 1)' + 2(x- 1) if 1 < x < 2 2х - 1 if 2 < x < 3
Transcribed Image Text:Question 1 (a) A biologist who is studying the growth of a bacteria culture, recorded the following data 0369 p(t) 2 3 4 6 where p(t) denotes the number of bacteria at time t (minutes). Use natural cubic spline to estimate the number of bacteria at t = 5. (b) Consider the function Ax) = 1/(1+x²) (i) Construct the clamped cubic spline that interpolates the function at x = -2,-1,0,1 and 2. %3D (ii) Compare the interpolated values with the true values at x = -1.5,-0.5,0.5, and 1.5 (c) Determine whether the following function is a cubic spline -x² + 1 if 0 < x s 1 (x – 1)' + 2(x- 1) if 1 < x < 2 2х - 1 if 2 < x < 3
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