SolomonZelman
  • SolomonZelman
Just trying out... (the math there is just for me see the entirety of my latex)
LaTeX Practicing! :)
  • Stacey Warren - Expert brainly.com
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
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SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle \left.\int_{a}^{b} f(x)={\rm F}(x)\right|^{b}_{a}={\rm F}(b)-{\rm F}(a) }\)
SolomonZelman
  • SolomonZelman
Successful! ``` \(\large\color{black}{ \displaystyle \left.\int_{a}^{b} f(x) ={\rm F}(x)\right|^{b}_{a}={\rm F}(b)-{\rm F}(a) }\) ``` \(\color{red}{\text{\left.}}\) integral, blah blah \(\color{red}{\text{\right|}}\) \(\color{black}{\Uparrow}\) (Placed \(\color{red}{\text{\left.}}\) before the integral, and that works to make the line higher to make it look nicer)
Liv1234
  • Liv1234
@SolomonZelman Can you teach me how to do this if you have some time?

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SolomonZelman
  • SolomonZelman
I am not that good :)
Liv1234
  • Liv1234
It seems hard to do haha, so you seemed to do really good
SolomonZelman
  • SolomonZelman
\(\large\color{#A44999}{ \displaystyle \oint F(x){~\sf d}{\bf \ell}}\) Nice colors, http://www.w3schools.com/tags/ref_colorpicker.asp choose or make up. Again I am just trying out things on here
SolomonZelman
  • SolomonZelman
\(\large{\bbox[4px,#fff1ff ,border:2px solid red ]{\color{#660033}{ \left.\begin{matrix} ~~~x &~~ & i^x~ \\ \\[0.9em] ~~4k & | & i^{4k}=(i^4)^x=1^x=\color{blue}{1} \\[0.9em] ~~4k+1 & | & i^{4k+1}=i^{4k}\cdot i^{1} =1\cdot i =\color{blue}{i}\\[0.9em] ~~4k+2& | & i^{4k+2}=i^{4k} \cdot i^{2}=1\cdot(-1)=\color{blue}{-1}\\[0.9em] ~~ 4k+3 & | & i^{4k+3}=i^{4k} \cdot i^{3}=i^{4k} \cdot i^{2}\times i^{9} \\[0.9em]&&=1\cdot(-1)\cdot i =\color{blue}{-i} \\[0.9em] \end{matrix}\right. }}}\)
SolomonZelman
  • SolomonZelman
\(\large\color{#003366}{\displaystyle\lim_{x \rightarrow ~\infty }\left[\frac{x}{\ln(x!)}\right] }\) \(\large\color{#003366}{\displaystyle\lim_{x \rightarrow ~\infty }\left[\frac{x\ln(e)}{\ln(x!)}\right] }\) \(\large\color{#003366}{\displaystyle\lim_{x \rightarrow ~\infty }\left[\frac{\ln(e^x)}{\ln(x!)}\right] }\) \(\large\color{#003366}{\displaystyle \ln \left[\lim_{x \rightarrow ~\infty }\frac{e^x}{x!}\right]=0 }\)
SolomonZelman
  • SolomonZelman
\(\large\color{#660033}{\displaystyle\lim_{x \rightarrow ~\infty }\left[\frac{\left( \ln x\right)^{k+2}}{x}\right]\quad ;\quad k\in \mathbb{N} }\) \(\large\color{#660033}{\displaystyle\lim_{x \rightarrow ~\infty }\left[\frac{~\frac{d}{dx}~\left[\left( \ln x\right)^{k+2} \right]~}{\frac{dx}{dx}}\right] }\) \(\large\color{#660033}{\displaystyle\lim_{x \rightarrow ~\infty }\left[\frac{~(k+2)\left( \ln x\right)^{k+1}~\times \dfrac{1}{x} }{1}\right] }\) \(\large\color{#660033}{\displaystyle\lim_{x \rightarrow ~\infty }\left[\frac{~(k+2)\left( \ln x\right)^{k+1} }{x}\right]}\) and differentiate a (k+2) number of times... and this is how it goes. \(\large\color{#339966}{\displaystyle\lim_{x \rightarrow ~\infty }\left[\frac{~\left( \ln x\right)^{k+2} }{x}\right]}\) \(\large\color{#339966}{\displaystyle\lim_{x \rightarrow ~\infty }\left[\frac{~\dfrac{d^{k+2}}{dx^{k+2}}~\left( \ln x\right)^{k+2} }{1}\right]}\) \(\large\color{#339966}{\displaystyle\lim_{x \rightarrow ~\infty }\left[\frac{(k+2)! }{x}\right]=0}\)
SolomonZelman
  • SolomonZelman
the colors are awesome... (squeeze trm to prove this for non integer k, suppose that there is a positive noninteger S, and a positive integer A that is greater than S, such that: k
SolomonZelman
  • SolomonZelman
just in case, for math completion.

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