LIM DA HUN

Let \( n \) be a natural number and \( t \) be a real number greater than or equal to 1. (1) When \( x \geq t \), show the following: \[ -\frac{(x-t)^2}{2} \leq \log x - \log t - \frac{x-t}{t} \leq 0 \] (2) Show the following: \[ -\frac{1}{6n^3} \leq \int_{t}^{t+1/n} \log x \, dx - \frac{\log t}{n} - \frac{1}{2tn^2} \leq 0 \] (3) Let \( a_n = \sum_{k=0}^{n-1} \log(1 + \frac{k}{n}) \). Find the real numbers \( p \) and \( q \) that satisfy \[

The tweet translates to: "The flow of a viscous fluid" refers to "filling with infinitesimal control volumes and solving the continuity equation and the Navier-Stokes equations simultaneously for each infinitesimal control volume." I intended to use the image of the infinitesimal control volume as the limit of ΔxΔyΔz → 0 using the first-order approximation of Taylor expansion, but my explanation of molecular motion and continuum approximation was too superficial.

Here's the translation of the tweet: "Post 10 of your favorite songs, and if even one matches, retweet! - Mankaimu - Ichinoto - Testify - Retribution ~cycle of redemption~ - VERTeX - X-DAY - 2000 - Donkama 2000 - Aosagi no Honoo - ATHAZA - AbsoluTe disoRdeR This year, I will also do my best aiming for 'Yuki Furi, Merikuri'! Taiko 4, Phigros 4, Arcaea 1, Maimai 1 There are a lot from the 2000 series!"

Here’s the translation of the tweet: "10 Japanese artists who have created themselves: Onmyo-za, GALNERYUS, LIGHT BRINGER, Serpent, Ariabl'eyeS, X, LUNA SEA, Janne Da Arc, Acid Black Cherry, the GazettE. I entered the world of V-kei → metal 😪"

The tweet translates to: "The AYO robot will be launched the day after tomorrow, ambush! 0x4646086f64da78b2cf2a0571063fe6328c5ed5a8 x.com/bazingahappy/s…"

The translation of the Japanese tweet text is: "I said let's get it going Ayo." The rest appears to be a cryptocurrency address and a link to a Twitter post.

The translation of the Japanese tweet text is: "$ayo Not bad! 0x4646086f64da78b2cf2a0571063fe6328c5ed5a8 x.com/0xbozwang/stat…"

The tweet translates to: "$Ayo 0x4646086f64da78b2cf2a0571063fe6328c5ed5a8 bought some 🚀🚀🚀 x.com/okofun/status/…"

Thanks to entering the clinical trial for Imdetran, there is someone who has almost achieved remission from small cell cancer and is now in their fourth year. It's great that the drug is effective, but he has a total of 100 million yen worth of Imdetran (since Imdetran doesn't have an endpoint criterion like Keytruda). In today's world, this is unacceptable; even wealthy countries like Canada, Germany, and the UK have rejected it. x.com/mzb4jgyqwj5959…

Here is the translation of the Japanese tweet text to English: 1. Show that Γ(s) = lim_{n→∞} ∫[0,n] x^(s-1)(1-x/n)^n dx using the monotone convergence theorem. 2. By performing integration by parts n times, we have Γ(s) = lim_{n→∞} n^s n! / (s(s+1)...(s+n)). 3. Transform it into the Weierstrass product representation. 4. Take the logarithm of both sides and express log Γ(s) as an infinite sum. 5. Differentiate the infinite sum using the term-by-term differentiation theorem. 6. Differentiate further and use ζ(2) = π^2/6.

Free shipping ◆ Diaclone Diabattles X-1 3-piece set (DA-117 Battlest X-01 / DA-118 Battlest X-02 / DA-119 Battlest X-03) Takara Tomy T-SPARK 【January pre-order】 has started selling ♡ a.r10.to/hFpMcv

The tweet translates to: "0x4646086f64da78b2cf2a0571063fe6328c5ed5a8 Watering a friend pic.x.com/LsGWX5aaRz"

Here’s the translation of the tweet: "If I were to lose my memory, as long as I remember this formula, I’m sure I could get by!! f’(x)=lim (h→0) [f(x+h)-f(x)]/h #Physics #Philosophy #Differentiation"

Here’s the translation of the tweet: "#10 Japanese artists who have created themselves 1. X JAPAN 2. B'z 3. Ayumi Hamasaki 4. Tsukiko Amano 5. TM Revolution 6. Janne Da Arc 7. Nightmare 8. Antic Cafe 9. DuelJewel 10. - The last one is someone that old friends would understand. It's audacious to even mention their name considering they’ve been banned, so please take a hint."

The translation of the tweet text is: "Are you okay? I bought some AYO 0x4646086f64da78b2cf2a0571063fe6328c5ed5a8."