5. *Let I = (-∞, 2) U (2, +∞) and consider the following real-valued functions defined on I. x²-4 1 f(x) = = 7²2²; 9(x) = ² x 1 h(x) = (a) Show that f does not have a limit as x→ 2. i.e. Prove the negation of the limit definition. x² 1 1 + x -2° (b) Show that g(x) and h(x) have limits as → 2. Your work should include a proof that these limits exist and you should find their values.
5. *Let I = (-∞, 2) U (2, +∞) and consider the following real-valued functions defined on I. x²-4 1 f(x) = = 7²2²; 9(x) = ² x 1 h(x) = (a) Show that f does not have a limit as x→ 2. i.e. Prove the negation of the limit definition. x² 1 1 + x -2° (b) Show that g(x) and h(x) have limits as → 2. Your work should include a proof that these limits exist and you should find their values.
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:5. *Let I = (-∞, 2) U (2, +∞) and consider the following real-valued functions defined on
I.
x²-4
1
f(x) = = 7²2²; 9(x) = ²
x
1
x²
1
h(x) =
(a) Show that f does not have a limit as x→ 2. i.e. Prove the negation of the limit
definition.
+
1
x-2
(b) Show that g(x) and h(x) have limits as → 2. Your work should include a proof that
these limits exist and you should find their values.
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