3. Let f(x) = re* sin(1/a) + a if a #0 (a) Prove if r E (-1,0) U (0, 1) then f(x)- |< e²]r]. (b) Prove by using the definition of a limit that lim f(r) = a.

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
3. Let f(x) re* sin(1/a) +o if a 0
(a) Prove if a E (-1,0) U (0, 1) then
(b) Prove by using the definition of a limit that lim /(r) = a.
f(e)-a<ex].
Transcribed Image Text:3. Let f(x) re* sin(1/a) +o if a 0 (a) Prove if a E (-1,0) U (0, 1) then (b) Prove by using the definition of a limit that lim /(r) = a. f(e)-a<ex].
Expert Solution
Step 1: Given.

Given: f(x)=xe2xsin1/x+α, if x0

To prove: a) x-1, 00, 1 then f(x)-α<e2x.

b) limx0f(x)=α, by using definition of limit.

steps

Step by step

Solved in 2 steps

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,