My Math Forum h(y) is a continuous function of y

 Real Analysis Real Analysis Math Forum

December 3rd, 2016, 11:32 AM   #1
Newbie

Joined: Dec 2016
From: Birmingham

Posts: 2
Thanks: 0

h(y) is a continuous function of y

I have attached JPG file with the question. Chapter 14 is Integrals on Rectangles and 14.2 is Fubini’s Theorem. But we can not use Fubini’s Theorem because we prove it two problems later in the book. I am completely lost and need help with writing a proof for the problem.
Attached Images
 14.2.1.JPG (22.3 KB, 18 views)

 December 5th, 2016, 05:39 PM #2 Senior Member   Joined: Sep 2016 From: USA Posts: 169 Thanks: 79 Math Focus: Dynamical systems, analytic function theory, numerics $f$ is continuous on $R$ so for $\eta = \frac{\epsilon}{b-a}$, there exists $\delta$ such that $|f(x,y) - f(x,z)| < \eta$ if $|y-z| < \eta$. Can you get a bound on $|h(y - \delta) - h(y + \delta)|$? As a hint, this is given explicitly by $\left| \int_a^b f(x,y-\delta) \ dx - \int_a^b f(x,y+\delta) \ dx \right|$

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post noobinmath Calculus 6 September 4th, 2015 10:20 PM Mahboob Math 1 March 14th, 2015 06:25 AM sebaflores Real Analysis 1 October 8th, 2013 11:23 AM OriaG Calculus 3 February 9th, 2013 04:35 PM frankpupu Calculus 5 February 13th, 2012 03:58 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top