a) The derivative of a function f(x) at a particular value of x can be approximately calculated by f'(x) = f(x+h)-f(x) h For f(x) = 7e0.5x and h = 0.3, find: i. ii. iii. the approximate value of f'(2). the true value of f'(2). the absolute and relative errors for part (i). b) Given the following operation: 50.36 41.13 +0.001 - 13.393 Compute the most accurate value for the operation where each number has been rounded to the certain decimal points.
a) The derivative of a function f(x) at a particular value of x can be approximately calculated by f'(x) = f(x+h)-f(x) h For f(x) = 7e0.5x and h = 0.3, find: i. ii. iii. the approximate value of f'(2). the true value of f'(2). the absolute and relative errors for part (i). b) Given the following operation: 50.36 41.13 +0.001 - 13.393 Compute the most accurate value for the operation where each number has been rounded to the certain decimal points.
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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Transcribed Image Text:a) The derivative of a function f(x) at a particular value of x can be approximately
calculated by
f'(x) = f(x+h)-f(x)
h
For f(x) = 7e0.5x and h = 0.3, find:
the approximate value of f'(2).
the true value of f'(2).
the absolute and relative errors for part (i).
i.
ii.
iii.
b) Given the following operation:
50.36 41.13 +0.001 - 13.393
Compute the most accurate value for the operation where each number has been
rounded to the certain decimal points.
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