Introduction To Calculus And Analysis

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I believe it is not necessary to read the previous pages and the book first as my problem is manipulation and not concepts.

Introduction To Calculus And Analysis

I can follow the manipulation, but the confusion is how he came to the conclusion

Schaum’s Outlines Advanced Calculus Second Edition Softcover Reference Book Textbook Vintage

Judging from the text, you are not expected to come up with this formula for $delta$ at this point, or any other suitable formula. The appearance here is just for show: just to show that there’s a formula to make it work.

. Working with the definition of the $epsilon$-$delta$ boundaries is not a “solve for $delta$” problem. If there is a limit, there is a whole range of values ​​for $delta$ that will suffice, and as long as you find

Note that a more general technique is to require $δ=min(1, bar δ)$ so that one can extract a linear factor $δ$ and bind all $δ$ into the remaining factor $1$, $$ to δ. (2|x_0|+δ)le bar δ(2|x_0|+1). $$ has a limit $ϵ$ if $bar δ=frac$ is chosen. All in all, $$ δ=minleft(1, fracright) $$ is a valid choice.

One may have difficulty determining which of these limits is the smallest (actually “$+$” in terms of the concavity of a square root). However, since neither is zero, the expression “$min$” is sufficient for the proof.

Fractional Calculus Of Variations In Terms Of A Generalized Fractional Integral With Applications To Physics

As indicated in the comments, to satisfy the going concern assumption, $|f(x)-f(y)|<epsilon$ for which we can put $delta(2|x_0+delta )<epsilon$ which is a quadratic inequality, which gives us the given value of $delta$

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