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Problem. Let zy(r²–y²) 7+y² if x + 0 f (x) = if x = 0 (1) Show that f, D\f, and D2f are continuous on R². WHAT THIS MEANS YOU MUST DO (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 S? if x +0 ? if x = 0 (Dif) (x) = S? if x +0 (D2f)(x) if x = 0 (e) Show lim (Dif)(x) = (Dif)(0). Show lim (D2f) (x) = (D2f)(0)

Problem. Let zy(r²–y²) 7+y² if x + 0 f (x) = if x = 0 (1) Show that f, D\f, and D2f are continuous on R². WHAT THIS MEANS YOU MUST DO (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 S? if x +0 ? if x = 0 (Dif) (x) = S? if x +0 (D2f)(x) if x = 0 (e) Show lim (Dif)(x) = (Dif)(0). Show lim (D2f) (x) = (D2f)(0)

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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Solve Problem 4.6.1

Problem. Let zy(r²-v²) { if x + 0 f (x) = if x = 0 (1) Show that f,Dıf, and D2f are continuous on R?. WHAT THIS MEANS YOU MUST DO (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 J? if x +0 (Dif)(x) = |? if x = 0 J? if x +0 (Daf) (x) = if x = 0 (e) Show lim (Dif)(x) = (Dif) (0). Show lim (D2f)(x) = (D2f) (0)
Transcribed Image Text:Problem. Let zy(r²-v²) { if x + 0 f (x) = if x = 0 (1) Show that f,Dıf, and D2f are continuous on R?. WHAT THIS MEANS YOU MUST DO (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 J? if x +0 (Dif)(x) = |? if x = 0 J? if x +0 (Daf) (x) = if x = 0 (e) Show lim (Dif)(x) = (Dif) (0). Show lim (D2f)(x) = (D2f) (0)
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