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.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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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.
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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