[Tex/LaTex] Why fraction (with power) in fraction doesn’t work

fractions

$$\lim_{x\to 0^{+}} \frac{e^{-\frac{1}{x}}{x^{10}}$$

here is my code. It said,

Emergency stop.
<*> Worksheet2_main

!  ==> Fatal error occurred, no output PDF file produced!
Transcript written on ./Worksheet2_main.log.
***------------------------------------------------------------
*** Running bibtex on Worksheet2_main ...
***------------------------------------------------------------

So I tried to write the numerator by its own.

$$e^{-\frac{1}{x}$$

It just works. How could this happen?

Best Answer

The error message is issued because the numerator part of the fractional expression isn't terminated with a } (closing curly brace).

You should also contemplate inline-fraction notation, {-1/x}, for the exponent of e. The resulting expression will be both more compact and easier to read as the terms are typeset in script style rather than in scriptscript style.

Finally, note that using $$ to start and end display-math mode is deprecated in LaTeX; use \[ and \] instead. For more information on this subject, see Why is \[ ... \] preferable to $$ ... $$?

\documentclass{article} 
\begin{document}
\[
\lim_{x\to 0^{+}} \frac{e^{-\frac{1}{x}}}{x^{10}} =
\lim_{x\to 0^{+}} \frac{e^{-1/x}}{x^{10}}
\]
\end{document}

Related Solutions

[Tex/LaTex] Fraction with doubled line

Use either \Tfrac or \Dfrac (short for Text and Display style "equal fraction") in the following:

enter image description here

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\usepackage{xcolor}% http://ctan.org/pkg/xcolor
\newcommand{\Tfrac}[2]{%
  \ooalign{%
    $\genfrac{}{}{1.2pt}1{#1}{#2}$\cr%
    $\color{white}\genfrac{}{}{.4pt}1{\phantom{#1}}{\phantom{#2}}$}%
}
\newcommand{\Dfrac}[2]{%
  \ooalign{%
    $\genfrac{}{}{1.2pt}0{#1}{#2}$\cr%
    $\color{white}\genfrac{}{}{.4pt}0{\phantom{#1}}{\phantom{#2}}$}%
}
\begin{document}
$f(x)=\Tfrac{1}{2}+\frac{1}{2}$
\end{document}

For a short course on \ooalign, see \subseteq + \circ as a single symbol (“open subset”).

Here is a slightly modified set of commands: \Efrac and \efrac. While both adjust their fraction size based on the math style automatically (using \mathchoice), the former is vertically higher (set based on the height of the two outer black fraction lines) than the latter (set based on the height of a regular fraction).

enter image description here

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\usepackage{xcolor}% http://ctan.org/pkg/xcolor
\newcommand{\Efrac}[2]{%
  \mathchoice
    {\ooalign{%
      $\genfrac{}{}{1.2pt}0{#1}{#2}$\cr%
      $\color{white}\genfrac{}{}{.4pt}0{\phantom{#1}}{\phantom{#2}}$}}%
    {\ooalign{%
      $\genfrac{}{}{1.2pt}1{#1}{#2}$\cr%
      $\color{white}\genfrac{}{}{.4pt}1{\phantom{#1}}{\phantom{#2}}$}}%
    {\ooalign{%
      $\genfrac{}{}{1.2pt}2{#1}{#2}$\cr%
      $\color{white}\genfrac{}{}{.4pt}2{\phantom{#1}}{\phantom{#2}}$}}%
    {\ooalign{%
      $\genfrac{}{}{1.2pt}3{#1}{#2}$\cr%
      $\color{white}\genfrac{}{}{.4pt}3{\phantom{#1}}{\phantom{#2}}$}}%
}
\newcommand{\efrac}[2]{%
  \mathchoice
    {\ooalign{%
      $\genfrac{}{}{1.2pt}0{\hphantom{#1}}{\hphantom{#2}}$\cr%
      $\color{white}\genfrac{}{}{.4pt}0{\color{black}#1}{\color{black}#2}$}}%
    {\ooalign{%
      $\genfrac{}{}{1.2pt}1{\hphantom{#1}}{\hphantom{#2}}$\cr%
      $\color{white}\genfrac{}{}{.4pt}1{\color{black}#1}{\color{black}#2}$}}%
    {\ooalign{%
      $\genfrac{}{}{1.2pt}2{\hphantom{#1}}{\hphantom{#2}}$\cr%
      $\color{white}\genfrac{}{}{.4pt}2{\color{black}#1}{\color{black}#2}$}}%
    {\ooalign{%
      $\genfrac{}{}{1.2pt}3{\hphantom{#1}}{\hphantom{#2}}$\cr%
      $\color{white}\genfrac{}{}{.4pt}3{\color{black}#1}{\color{black}#2}$}}%
}
\begin{document}
\[ f(x)={\textstyle\Efrac{1}{2}+\frac{1}{2}} \sim \Efrac{3}{4}+\frac{3}{4} \]
\[ f(x)={\textstyle\efrac{1}{2}+\frac{1}{2}} \sim \efrac{3}{4}+\frac{3}{4} \]
\end{document}

[Tex/LaTex] Fraction within another fraction

You can use \cfrac for nested fractions. However this makes the ‘upper’ denominators too close from the main fraction line, so one can compensate adding a phantom letter with descenders. No compensation required for the ‘lower’ numerators if you use \cfrac (not \dfrac).

Another possibility would use the \mfrac(medium-sized fraction – 80 % of \displaystyle) command from nccmath, so the smaller fractions are still readable. Here is an example of both methods:

\documentclass{article}
\usepackage{amsmath, nccmath}

\begin{document}

    \begin{align*}
        \frac{\sin(a+b)}{\cos(a+b)}&=\frac{\sin a \cos b + \cos a \sin b}{\cos a \cos b - \sin a \sin b}
        \\
        \tan(a+b)&=\frac{\sin a \cos b + \cos a \sin b}{\cos a \cos b - \sin a \sin b}
        \\[0.5ex]
        &=\frac{\cfrac{\sin a \cos b}{\cos a \cos b} + \cfrac{\cos a \sin b}{\cos a \cos b\vphantom{g}}}{\cfrac{\cos a \cos b}{\cos a \cos b} - \cfrac{\sin a \sin b}{\cos a \cos b}}
        \\[0.5ex]
        &=\frac{\cfrac{\sin a}{\cos a} + \cfrac{\sin b}{\cos b \vphantom{g}}}{1 - \cfrac{\sin a \sin b}{\cos a \cos b}}
        \\[0.5ex]
        &=\frac{\tan a +\tan b }{1 - \tan a \tan b}
    \end{align*}\medskip

    \begin{align*}
        \frac{\sin(a+b)}{\cos(a+b)}&=\frac{\sin a \cos b + \cos a \sin b}{\cos a \cos b - \sin a \sin b}
        \\
        \tan(a+b)&=\frac{\sin a \cos b + \cos a \sin b}{\cos a \cos b - \sin a \sin b}
        \\[0.5ex]
        &=\frac{\mfrac{\sin a \cos b}{\cos a \cos b} + \mfrac{\cos a \sin b}{\cos a \cos b\vphantom{g}}}{\mfrac{\cos a \cos b}{\cos a \cos b} - \mfrac{\sin a \sin b}{\cos a \cos b}}
        \\[0.5ex]
        &=\frac{\mfrac{\sin a}{\cos a} + \mfrac{\sin b}{\cos b\vphantom{g}}}{1 - \mfrac{\sin a \sin b}{\cos a \cos b}}
        \\[0.5ex]
        &=\frac{\tan a +\tan b }{1 - \tan a \tan b}
    \end{align*}

\end{document}

Best Answer

Related Solutions

[Tex/LaTex] Fraction with doubled line

[Tex/LaTex] Fraction within another fraction

Related Question