If f is C2 on an interval prove that f(2 + k) – 2/(2) + {(z =A) = r"(2). - lim h-0 h2 = f"(x). The expression f(x+h) – 2f(x) +f(x-h) is called the symmetric second difference.
If f is C2 on an interval prove that f(2 + k) – 2/(2) + {(z =A) = r"(2). - lim h-0 h2 = f"(x). The expression f(x+h) – 2f(x) +f(x-h) is called the symmetric second difference.
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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![If \( f \) is \( C^2 \) on an interval, prove that
\[
\lim_{{h \to 0}} \frac{{f(x+h) - 2f(x) + f(x-h)}}{{h^2}} = f''(x).
\]
The expression \( f(x+h) - 2f(x) + f(x-h) \) is called the **symmetric second difference**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F25c0adaf-ce2a-47ff-8e03-556fe3b6cd55%2Fafdeb27a-12cd-488a-8eb9-508762137372%2Frggembr_processed.png&w=3840&q=75)
Transcribed Image Text:If \( f \) is \( C^2 \) on an interval, prove that
\[
\lim_{{h \to 0}} \frac{{f(x+h) - 2f(x) + f(x-h)}}{{h^2}} = f''(x).
\]
The expression \( f(x+h) - 2f(x) + f(x-h) \) is called the **symmetric second difference**.
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