We know that if f is differentiable, we can write the derivative function as f(x+ h) – f(x) f'(x) = lim h→0 h Hypothesize what lim h→0 f(x+h) – 2f(x) + f(x – h) h2 should represent. Try to convince the reader that your hypothesis is correct. For example, you could compute the above limit for several choices of f and show that the answer agrees with your hypothesis.
We know that if f is differentiable, we can write the derivative function as f(x+ h) – f(x) f'(x) = lim h→0 h Hypothesize what lim h→0 f(x+h) – 2f(x) + f(x – h) h2 should represent. Try to convince the reader that your hypothesis is correct. For example, you could compute the above limit for several choices of f and show that the answer agrees with your hypothesis.
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:We know that if f is differentiable, we can write the derivative function as
f(x+ h) – f(x)
|
f'(x) = lim
h→0
h
Hypothesize what lim
h→0
f(x+ h) – 2f(x)+ f(x – h)
h2
should represent. Try to convince the reader
that your hypothesis is correct. For example, you could compute the above limit for several choices
of f and show that the answer agrees with your hypothesis.
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