1. [10 pts] Let f e C([a, b]). Suppose that f(x)g(x) dr = 0 a for all g e C([a, b]). Prove that f(x) = 0 for all r E [a, b]. Does the conclusion hold...
View the step-by-step solution to:

Question

ques 1 takehome 7.png

For all g on C([a,b]) this implies g(x)=

0.Prove that f(x) = 0 for all x om [a,b]. If, f is Riemann integrable on [a,b]?

ques 1 takehome 7.png

1. [10 pts] Let f e C([a, b]). Suppose that
f(x)g(x) dr = 0
a
for all g e C([a, b]). Prove that f(x) = 0 for all r E [a, b]. Does the conclusion hold if f is Riemann
integrable on [a, b]?

Top Answer

1) If f(x) is not zero at some point x 0 in (a, b), then there is d>0 such that (x 0 -d, x 0 +d) is a subset of [a, b] and... View the full answer

Sign up to view the full answer

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question