Betty Mock
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 Dec31 awarded Nice Answer Nov22 comment Does L'Hôpital's work the other way? Expand the top and bottom in a Taylor's polynomial. If the first term of both polynomials is zero, then you look at the second term. If both of those are zero, you go on to the third term, etc. Sooner or later you get a term which is not zero, and that is the one which shows you the limit. Aug5 awarded Yearling Feb20 answered Functions and Infinitesimals? Feb20 comment “Ito-Riemann” integration have you checked out this question: math.stackexchange.com/questions/426786/… Jan23 comment Existence of a Bound Related to Erratically Converging Sequences? Certainly once you pick $\epsilon$ you must be able to find an N so that for n > N the elements are within $\epsilon$ of the limit. For every sequence you have to pick N big enough to achieve that. I believe my construction meets that requirement, because the jumps are getting smaller with each $2^n$. So for any given $\epsilon$ the jumps of $2^{-n}$ will eventually (for large enough n) put the entire tail of the sequence in the epsilon neighborhood of the limit; but you will still get all those erratic elements -- more and more as $n \rightarrow \infty$. Jan23 comment $n^{th}$ root of a matrix. @mtiano Why would the existence of the root depend on the sign of the eigenvalues? Are we not admitting complex numbers? Also, if the matrix is not invertible the nth roots are still there even though those entries are zero; and the matrix is not expressible in exponential form. As per answer below, I was moving towards Jordan form -- if you can find the roots of a diagonalizable matrix, so too can you find the roots of the matrix in Jordan form. Jan22 comment $n^{th}$ root of a matrix. Continue with your diagonalization idea. If the matrix is diagonalizable can you say something about its roots? Jan19 comment Integral Operator Theory on $L^2[0,1]$ Would like to help you be warmer, etc. but I actually couldn't quite make my way thru your notation. Can you rewrite this with latex? See this site for assistance:physicsforums.com/showpost.php?p=3977517&postcount=3 Jan17 answered How do we prove the error estimation of the rectangle method Jan16 comment What is the limit of difference between harmonic series and natural logarithm of n+1? @KonstaNtie if you were me you'd be hitting your head because 25 is not divisible by 3. I think head hitting in your case is not appropriate. I'll upvote Sami's answer for you (and me). Jan16 comment Infinite Sum of factorial denominator and exponential numerator nicely explained Jan16 comment graphing $f(x)=x \ln \left(1+\frac{1}{x}\right)$ @user115947 your current problem is to find a tactful way to convey Andre Nicolas' comment to your teacher. Unfortuantely this site is about math, not tact. Jan16 revised Basic proof problem from “How to Prove it A Structured Approach” fixed mistake Jan16 comment Basic proof problem from “How to Prove it A Structured Approach” @DennisMeng plz ignore previous comment, I misread what you were saying. You are entirely right. Jan16 comment Basic proof problem from “How to Prove it A Structured Approach” @darkradeon sorry I misunderstood your question. see revised answer Jan16 revised Basic proof problem from “How to Prove it A Structured Approach” extended Jan16 comment Basic proof problem from “How to Prove it A Structured Approach” @DennisMeng gee I did say x > 1. Did you miss it? Since OP had a base of 2, we were in good shape. Jan16 comment Basic proof problem from “How to Prove it A Structured Approach” @darkradeon $2^3 -1$ = 7 which is exactly $2^2 + 2 + 1$ and $2^5$ checks out similarly at 31. So I don't get why you couldn't get them to match up. 2-1 = 1 of course. I understand about failing at square 1; I hope you are at least at square 2 now. Jan15 comment Would like help with a contour integral. I take it that $\rho$ is the radius of your circle? What is z in your second integral -- should it not be in terms of $\theta$?. I do not see that integral going to 0 because if you ignore the i$\epsilon$ it is essentially the integral of $e^{-izt}$. But do you want it to be 0? Shouldn't it add your step function?