因此,在附图中,文本“注意:‘积分变量’无关紧要”应与其下方的公式位于同一行。在代码中,我将所有内容放在一行上,但显示方式并非如此。其上方的公式和中间的所有公式都需要左对齐。我尝试过 flalign 和 align,但 flalign 只会给我错误,并且出于某种原因 align 不起作用。
以下是我想要在一行上显示的全部代码:Note: The "variable of integration" is irrelevant. $$\int_{-2}^{5} x^3 dx = \int_{-2}^{5} y^3 dy = \int_{-2}^{5} t^3 dt = ...$$
我只需要将一些公式左对齐,并在右侧留出一点缩进空间,以使其显示与文本不同。
谢谢
这是我的完整代码:
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath}
\documentclass[fleqn]{article}
\setlength{\mathindent}{0pt}
\begin{document}
\section{1 Limit of a Riemann Sum}Suppose $f$ is defined on [$a,b$] and $L$ is a real number. We write \\ $$\int_{a}^{b} f(x) dx = \lim_{|| P ||\to\ 0} \sum\limits_{k=1}^n f(C_k)\Delta \chi _k = L$$
if for every $\epsilon$ $>$ 0, there is a $\delta$ $>$ 0 so that if $P$ is any partition of [$a,b$] with $\left\Vert\left P \left\Vert\left $ $<$ $\delta$ and each $C_k$ is a number in the $k$th subinterval of $P$, then
$$\left\vert\left \sum\limits_{k=1}^n f(C_k)\Delta \chi _k - L \right\vert\right \textless \thinspace \thinspace \epsilon$$
\\
\\
\newline Note: The "variable of integration" is irrelevant. $$\int_{-2}^{5} x^3 dx = \int_{-2}^{5} y^3 dy = \int_{-2}^{5} t^3 dt = ...$$
\\
Ex: Do the following exist?
\\
\begin{flalign}
$$\left \int_{1}^{3} \frac{1}{x^2} dx$$ &&
\\&&
$$\left \int_{0}^{2} \frac{1}{x^2} dx$$&&
\end{flalign}
\\
\\
Ex: Evaluate $$\int_{1}^{4} f(x) dx$$ where $f(x)$ =
\end{flalign}
\\
\begin{cases}
$$3x^2 + 1, \quad 1 \leq x \leq 3$$
\\
$$28, \quad \quad \quad \quad 3$$ $<$ $$x \leq 4$$
\end{cases}
\\
\\
\\
You may use the fact that $$\int_{1}^{3} x^2 dx = \frac{26}{3}$$ where $f(x)$
\section{Miscellaneous Trivia}
Prove: If A $$\subseteq B, then \quad A \cap C \subseteq B \cap C$$
\\
\\
Fact: $C(n,r)$ = \Bigg(\overset{n}{r}\Bigg) = $$\frac{P(n,r)}{r!} = \frac{\frac{n!}{(n-r)!}}{r!} = \frac{n!}{r!(n-r)!}$$
\end{document}
答案1
发布的代码产生错误
! LaTeX Error: Two \documentclass or \documentstyle commands.
因为有两个\documentclass
如果你注释掉第二个,你会得到错误
! Undefined control sequence.
<argument> \mathindent
l.6 \setlength{\mathindent}{0pt}
因为长度没有定义
注释掉该行,你会得到错误
! Missing delimiter (. inserted).
<to be read again>
$
l.11 ... with $\left\Vert\left P \left\Vert\left $
$<$ $\delta$ and each $C_...
\left
公式末尾出现。如果您滚动过去,则会收到错误,提示没有匹配项,\right.
\left
并且\right
必须在同一表达式中成对匹配。
如果你修复了不匹配的问题\left
,那么你就会得到
! Missing } inserted.
<inserted text>
}
l.30 \end{flalign}
正如您所见$
,flalign
这是错误的,因为falign
已经进入数学模式。
如果你修复了嵌套数学,你会得到错误
! LaTeX Error: There's no line here to end.
出现\\
,但不能强制在没有行的地方换行,所以删除这些,这也会删除警告
Underfull \hbox (badness 10000) in paragraph at lines 18--22
这些是\\
错误放置在段落末尾的
然后你得到错误
! Missing $ inserted.
<inserted text>
$
l.44 Fact: $C(n,r)$ = \Bigg(\overset{n}{r}
因为您在 = 之前完成了数学运算,所以 = 后面的数学模式命令会产生错误。
修复该问题最终会生成一个无错误的日志。只有在此时,您才应该查看生成的 PDF,因为 TeX 在发生错误后不会尝试生成合理的 PDF 输出,它只会恢复足够的内容以检查剩余文档的语法,如果您滚动浏览错误,它不会生成可用的输出。
更改$$
为\[
然后导致此文档
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath}
%\documentclass[fleqn]{article}
%\setlength{\mathindent}{0pt}
\begin{document}
\section{1 Limit of a Riemann Sum}
Suppose $f$ is defined on [$a,b$] and $L$ is a real number. We write
\[\int_{a}^{b} f(x) dx = \lim_{|| P ||\to\ 0} \sum\limits_{k=1}^n f(C_k)\Delta \chi _k = L\]
if for every $\epsilon$ $>$ 0, there is a $\delta$ $>$ 0 so that if $P$ is any partition
of [$a,b$] with $\lVert P \rVert < \delta$ and each $C_k$ is a number
in the $k$th subinterval of $P$, then
\[\left\vert \sum\limits_{k=1}^n f(C_k)\Delta \chi _k - L \right\vert < \epsilon\]
Note: The "variable of integration" is irrelevant.
\[\int_{-2}^{5} x^3 dx = \int_{-2}^{5} y^3 dy = \int_{-2}^{5} t^3 dt = ...\]
Ex: Do the following exist?
\begin{flalign}
\int_{1}^{3} \frac{1}{x^2} dx &&
\\&&
\int_{0}^{2} \frac{1}{x^2} dx&&
\end{flalign}
Ex: Evaluate $$\int_{1}^{4} f(x) dx$$ where $f(x)$ =
\[\begin{cases}
3x^2 + 1, \quad 1 \leq x \leq 3
\\
28, \quad \quad \quad \quad 3<x \leq 4
\end{cases}
\]
You may use the fact that $$\int_{1}^{3} x^2 dx = \frac{26}{3}$$ where $f(x)$
\section{Miscellaneous Trivia}
Prove: If A
\[\subseteq B, then \quad A \cap C \subseteq B \cap C\]
Fact:
\[C(n,r) = \Bigg(\overset{n}{r}\Bigg) =
\frac{P(n,r)}{r!} =
\frac{\frac{n!}{(n-r)!}}{r!} =
\frac{n!}{r!(n-r)!}\]
\end{document}
即
添加fleqn
到\documentclass
将使显示的表达式左对齐,并且所有表达式(例如)$\epsilon$ $>$ 0
都应排版为单个数学表达式,以便获得正确的间距,并且最后的 0 在数学内部,因此$\epsilon > 0$
,在显示数学之前也永远不会有空行。
最后得到这个,这可能是你所需布局的近似值,我不得不做一些猜测
\documentclass[fleqn]{article}
\usepackage[utf8]{inputenc}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath}
%\documentclass[fleqn]{article}
%\setlength{\mathindent}{0pt}
\begin{document}
\section{1 Limit of a Riemann Sum}
Suppose $f$ is defined on [$a,b$] and $L$ is a real number. We write
\[\int_{a}^{b} f(x) dx = \lim_{|| P ||\to\ 0} \sum\limits_{k=1}^n f(C_k)\Delta \chi _k = L\]
if for every $\epsilon > 0$, there is a $\delta >0$ so that if $P$ is any partition
of $[a,b]$ with $\lVert P \rVert < \delta$ and each $C_k$ is a number
in the $k$th subinterval of $P$, then
\[\left\vert \sum\limits_{k=1}^n f(C_k)\Delta \chi _k - L \right\vert < \epsilon\]
Note: The "variable of integration" is irrelevant.
\[\int_{-2}^{5} x^3 dx = \int_{-2}^{5} y^3 dy = \int_{-2}^{5} t^3 dt = ...\]
Ex: Do the following exist?
\begin{gather}
\int_{1}^{3} \frac{1}{x^2} dx\\
\int_{0}^{2} \frac{1}{x^2} dx
\end{gather}
Ex: Evaluate \[\int_{1}^{4} f(x) dx\] where
\[f(x) =
\begin{cases}
3x^2 + 1, \quad 1 \leq x \leq 3\\
28, \quad \quad \quad \quad 3<x \leq 4
\end{cases}
\]
You may use the fact that
\[\int_{1}^{3} x^2 dx = \frac{26}{3}\]
where $f(x)$
\section{Miscellaneous Trivia}
Prove: If
\[A\subseteq B, then \quad A \cap C \subseteq B \cap C\]
Fact:
\[C(n,r) = \Bigg(\overset{n}{r}\Bigg) =
\frac{P(n,r)}{r!} =
\frac{\frac{n!}{(n-r)!}}{r!} =
\frac{n!}{r!(n-r)!}\]
\end{document}