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
icon
Related questions
Question
No Handwritin
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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 5 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,