6. Suppose f and g are functions with domain R. If both f and g are even but f+g is odd, then prove that g(x) = -f(x) for all r ER.

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
6. Suppose f and g are functions with domain R. If both f and g are even but f+g is odd,
then prove that g(x) = -f(x) for all r ER.
%3D
7. Suppose neither lim f(x) nor lim g(x) exists. Show that lim f(x)g(x)] may exist.
x – 4
8. Prove that lim Va = 2 using the e-d-definition.
Hint: Va - 2 =
%3D
VI +2
9. Suppose g is a function continuous at c and g(c) > 0. Prove that there exists 8>0 such
that g(x) >0 for all r E (c- 8, c+ 8).
10. Consider the function
if r E Q
f (x) =
if x Q.
Prove that f'(0) = 0.
Hint: The fact stated in Question 10 of Problem Set 2 is useful.
Transcribed Image Text:6. Suppose f and g are functions with domain R. If both f and g are even but f+g is odd, then prove that g(x) = -f(x) for all r ER. %3D 7. Suppose neither lim f(x) nor lim g(x) exists. Show that lim f(x)g(x)] may exist. x – 4 8. Prove that lim Va = 2 using the e-d-definition. Hint: Va - 2 = %3D VI +2 9. Suppose g is a function continuous at c and g(c) > 0. Prove that there exists 8>0 such that g(x) >0 for all r E (c- 8, c+ 8). 10. Consider the function if r E Q f (x) = if x Q. Prove that f'(0) = 0. Hint: The fact stated in Question 10 of Problem Set 2 is useful.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 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,