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6. If af/ax is continuous on the rectangle R = {(t, x): 0 ≤ t - to| 0 such that |f(t, x₁) = f(t, x2)| ≤ Kx1 - x2| for all (t, x₁) and (t, ₂) in R.

6. If af/ax is continuous on the rectangle R = {(t, x): 0 ≤ t - to| 0 such that |f(t, x₁) = f(t, x2)| ≤ Kx1 - x2| for all (t, x₁) and (t, ₂) in R.

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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6. If af/ax is continuous on the rectangle R = {(t, x): 0 ≤ |t - to| <a, 0 ≤|x − xo| <b}, prove that there exists a K > 0 such that |ƒ(t, x₁) — ƒ(t, x2)| ≤ K|X1 − X2| - for all (t, x₁) and (t, x₂) in R.
Transcribed Image Text:6. If af/ax is continuous on the rectangle R = {(t, x): 0 ≤ |t - to| <a, 0 ≤|x − xo| <b}, prove that there exists a K > 0 such that |ƒ(t, x₁) — ƒ(t, x2)| ≤ K|X1 − X2| - for all (t, x₁) and (t, x₂) in R.
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