Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Calculus and Beyond Homework Help
Proving Uniqueness in Continuous Functions with Positive Values
Reply to thread
Message
[QUOTE="proximaankit, post: 4506162, member: 483877"] [h2]Homework Statement [/h2] Suppose that k(t) is a continuous function with positive values. Show that for any t (or at least for any t not too large), there is a unique τ so that τ =∫ (k(η)dη,0,t); conversely any such τ corresponds to a unique t. Provide a brief explanation on why there is such a 1-1 correspondence. [h2]Homework Equations[/h2] NA [h2]The Attempt at a Solution[/h2] Stuck on it but here are some of my thoughts and reasoning: I first view τ as function dependent upon t. since k(t) is positive and continuous, that will mean that the antiderivative of k(t) will only give us increasing values for increasing t. The new k(η) function is essentially same as k(t) except with η as the independent var. Hence since the k(t) is positive then k(η) is also positive. Then the integral of k(η) must be increasing for each increasing t. Hence for t[SUB]2[/SUB] and t[SUB]1[/SUB] the integral of k(η) from 0 to t[SUB]2[/SUB] is greater than the integral of k(η) from 0 to t[SUB]1[/SUB]. This makes sure the for every different t substitute into the integral have a different output. And as we said τ is The problem is how do I show the unique τ for each t part. Thank you very much in advance for any help :) [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Calculus and Beyond Homework Help
Proving Uniqueness in Continuous Functions with Positive Values
Back
Top