1. Using techniques in calculus, solve for the exact or true value of the derivative of the function below at x = 3. Show your complete manual solution. Save values while calculating but show/write and round your answer in 4 decimal places only. S(x) = 7xe®sx 2. Approximate the derivative of the function at x 3 by using f'(x) = Z«+h=/M at h = 0.3. 3. Find the true error for the approximation above. E, = true value – approximate value 4. Complete the table below. Approximate the derivative by completing the table using the different values of h given. Show your complete manual solution. approximate error = E, = present approximation – previous approximation approximate error t relative approximate error = 1%e,l = present approximationl absolute percent x 100 D 3 f(x) P(x) approximation present previous approximate approxim approxim absolute relative x+h f(x+h) error approximate error ation ation 5 0.3 6. 0.15 7 0.1 0.01 0.001 8 5. Complete the table using a spreadsheet software (e.g. MS Excel). You may use a mobile phone application. Approximate the derivative by completing the table using the different values of h given. Points will be given depending on how efficiently you utilized your spreadsheet software. 123
1. Using techniques in calculus, solve for the exact or true value of the derivative of the function below at x = 3. Show your complete manual solution. Save values while calculating but show/write and round your answer in 4 decimal places only. S(x) = 7xe®sx 2. Approximate the derivative of the function at x 3 by using f'(x) = Z«+h=/M at h = 0.3. 3. Find the true error for the approximation above. E, = true value – approximate value 4. Complete the table below. Approximate the derivative by completing the table using the different values of h given. Show your complete manual solution. approximate error = E, = present approximation – previous approximation approximate error t relative approximate error = 1%e,l = present approximationl absolute percent x 100 D 3 f(x) P(x) approximation present previous approximate approxim approxim absolute relative x+h f(x+h) error approximate error ation ation 5 0.3 6. 0.15 7 0.1 0.01 0.001 8 5. Complete the table using a spreadsheet software (e.g. MS Excel). You may use a mobile phone application. Approximate the derivative by completing the table using the different values of h given. Points will be given depending on how efficiently you utilized your spreadsheet software. 123
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
numerical methods
QUESTION NUMBER 5 ONLY!!
Transcribed Image Text:1. Using techniques in calculus, solve for the exact or true value of the derivative of
the function below at x = 3. Show your complete manual solution. Save values
while calculating but show/write and round your answer in 4 decimal places
only.
f(x) = 7xe0.5x
2. Approximate the derivative of the function at x = 3 by using f'(x) = Lx+h)-1(1)
at h = 0.3.
3. Find the true error for the approximation above. E = true value –
approximate value
4. Complete the table below. Approximate the derivative by completing the table
using the different values of h given. Show your complete manual solution.
approximate error = Ea = present approximation – previous approximation
approximate error
absolute percent relative approximate error = 1%cal =|
present approximation
x 100
A
B
D
E
3
f(x)
f(x) approximation
present previous approximate
f(x+h)
approxim approxim
absolute
relative
x+h
error
approximate
error
4
ation
ation
0.3
6
0.15
0.1
8.
0.01
9
0.001
5. Complete the table using a spreadsheet software (e.g. MS Excel). You may use a
mobile phone application. Approximate the derivative by completing the table
using the different values of h given. Points will be given depending on how
efficiently you utilized your spreadsheet software.
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