Suppose that there exists M> 0 and 8 >0 such that for all r = (a −8, a+6) \ {a}, f(x) = f(a)| ≤ Mx - aª. Show that when a > 1, then f is differentiable at a and when a > 0, f is continuous at a.
Suppose that there exists M> 0 and 8 >0 such that for all r = (a −8, a+6) \ {a}, f(x) = f(a)| ≤ Mx - aª. Show that when a > 1, then f is differentiable at a and when a > 0, f is continuous at a.
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:Suppose that there exists M> 0 and 8 >0 such that for all r = (a −8, a+6) \ {a},
f(x) = f(a)| ≤ Mx - aª.
Show that when a > 1, then f is differentiable at a and when a > 0, f is continuous at a.
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