(1) Show that f, Dif, and D2ƒ are continuous on R². WH (a) Show lim f (x) = f (0)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve Problem 4.6.1
Transcribed Image Text:Problem. Let
if x + 0
f (x)
2²+y?
if x = 0
(1) Show that f, Dif, and D2f are continuous on R?. WHAT THIS MEANS YOU MUST D0
(a) Show lim f (x) = f (0)
(b) Compute (Dif) (x) and (D2f) (x) for x + 0 using Calc3 methods. Briefly argue that
these are continuous for x + 0.
(c) Compute (Dif) (0) and (D2f)(0) using limits.
(d) Complete the following chart
[? if x +0
(Dif) (x)
if x = 0
(Da £) (x) = ? if x + 0
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