Recent content by bamajon1974

Good morning I have been refreshing my memory about Leibniz differentiation of integrals and found some useful videos from digital-university.org on YouTube. Although the audio quality is poor and the speaker proceeds a bit slowly, the explanations and processes are clear. However, it seems...

I think I see now. Equivalently, ##|a/b| = |a|/|b|.## In the context of my question, it is ##|a|/b##, since ## |a|=|x+3|## and ##|b|## is ##|5x^2|=5x^2## which always positive. Given that ##|x-3|<1## and ##|a/b| = |a|/|b|.##, I can find upper and lower bounds of the numerator and denominator...

This is an interesting way of finding delta in terms of epsilon, seems more general. Does this technique find the optimal delta range that works, as opposed to say, delta=min{1, 5*epsilon/4) which is just a delta range that works but not necessarily the optimal range? Also, in the second to...

Ok then I should clarify...I understand the process of bounding. The question I have is the algebra involved in bounding, i.e., is it legal to find the bounds f the numerator and denominator separately or as a single quotient. In the end, I found my bounds but the issue was just a side question...

I made a mistake in the original post and corrected. What I want to do is use $$|x-3|<1$$ to bound ##\frac{|x+3|}{5x^2}## and equal to some number.

I made a mistake and ##\frac{|x+3|}{5x^2}<A## for some number A to be determined, not 1. I am guessing you would have to consider the numerator and denominator separately. So for the numerator, ##5<x+3<7## and for the denominator, ##\frac{1}{80}<\frac{1}{5x^2}<\frac{1}{20}.## Then, can I...

How does one manipulate rational absolute inequalities? For example, I want to transform the absolute value inequality ##|x-3|<1## to ##\frac{|x+3|}{5x^2}<A \ ##, for some number ##\text{A}##, to find an upper and lower bound on the latter term using the constraint in the first term, and not...

Thank you. A few follow up questions...The part that I did as the scratch work that you suggest including in the proof, do you mean the line where I show ##|\frac{1}{x^2} - \frac{1}{4}| = \frac{|x-2||x+2|}{4x^2}## ? I would think the best place to show this work would be between the 5th and...

Woops. I found several errors. I was able to correct.

Summary:: Good afternoon. I have more questions about the details of epsilon-delta proofs. Below is a simple, rational limit proof example with questions at the end. The scratch work and proof are a bit pedantic but I don't follow proofs very well which omit a lot of details, including scratch...

I did find some mistakes. How do I correct the mistakes in the original post?

Good afternoon. I have some questions about the details of epsilon-delta proofs. Below is a simple, non-linear limit proof example which will serve as an example of the questions I have. The questions are below the example and involve clarification and explanations of steps and details in the...

This article helps. I will check it out. Do you know of a corresponding website for hyperbolic functions and their parallel trig functions as well? Do you happen to have the article referenced in the website? The pdf file doesn't seem to exist anymore...

Are there any useful references or resources that intuitively show how Jacobi Elliptic functions [sn, cn, dn, etc] are geometrically interpreted from properties of ellipses? And how the Jacobi Elliptic functions and integrals can be shown to be generalizations of circular trig functions? Thanks!