4. Suppose F: R" → R² is of the form F(r) = (f(x), g(x)), rE R". (i) Show that lim F(x) = (a, b) if and only if lim f(r) - a and lim alr) - b
4. Suppose F: R" → R² is of the form F(r) = (f(x), g(x)), rE R". (i) Show that lim F(x) = (a, b) if and only if lim f(r) - a and lim alr) - b
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 using epsilon deltas
Transcribed Image Text:4. Suppose F: R" → R? is of the form
F(r) = (f(x), g(x)), TE R".
(i) Show that
lim F(r) = (a,b)
if and only if
lim f(r) = a and
lim g(x) = b.
(ii) Show that F is continuous at ro if and only if f and g are both continuous
at 1o-
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