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-rw-r--r--Master/texmf-dist/doc/latex/probsoln/1stprncp.tex36
1 files changed, 3 insertions, 33 deletions
diff --git a/Master/texmf-dist/doc/latex/probsoln/1stprncp.tex b/Master/texmf-dist/doc/latex/probsoln/1stprncp.tex
index d7ccacdcda3..f857392a6ef 100644
--- a/Master/texmf-dist/doc/latex/probsoln/1stprncp.tex
+++ b/Master/texmf-dist/doc/latex/probsoln/1stprncp.tex
@@ -1,31 +1,4 @@
-%%
-%% This is file `1stprncp.tex',
-%% generated with the docstrip utility.
-%%
-%% The original source files were:
-%%
-%% probsoln.dtx (with options: `1stprncp.tex,package')
-%% Copyright (C) 2006 Nicola Talbot, all rights reserved.
-%% If you modify this file, you must change its name first.
-%% You are NOT ALLOWED to distribute this file alone. You are NOT
-%% ALLOWED to take money for the distribution or use of either this
-%% file or a changed version, except for a nominal charge for copying
-%% etc.
-%% \CharacterTable
-%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
-%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
-%% Digits \0\1\2\3\4\5\6\7\8\9
-%% Exclamation \! Double quote \" Hash (number) \#
-%% Dollar \$ Percent \% Ampersand \&
-%% Acute accent \' Left paren \( Right paren \)
-%% Asterisk \* Plus \+ Comma \,
-%% Minus \- Point \. Solidus \/
-%% Colon \: Semicolon \; Less than \<
-%% Equals \= Greater than \> Question mark \?
-%% Commercial at \@ Left bracket \[ Backslash \\
-%% Right bracket \] Circumflex \^ Underscore \_
-%% Grave accent \` Left brace \{ Vertical bar \|
-%% Right brace \} Tilde \~}
+% These all involve differentiating from 1st principles
\newproblem{dfp:xcube}{%
Differentiate $f(x) = x^3$ with respect to $x$ by first principles.}{%
@@ -71,7 +44,7 @@ Differentiate from first principles $f(x) = c$ where $c$ is a constant.}{%
\end{eqnarray*}}
\newproblem{dfp:cosx}{%
-Given
+Given
\begin{eqnarray*}
\lim_{x \rightarrow 0} \frac{\cos x - 1}{x} & = & 0\\
\lim_{x \rightarrow 0} \frac{\sin x}{x} & = & 1
@@ -82,10 +55,7 @@ differentiate from first principles $f(x) = \cos x$.}{%
& = & \lim_{\Delta x \rightarrow 0} \frac{\cos(x + \Delta x) - \cos(x)}{\Delta x}\\
& = & \lim_{\Delta x \rightarrow 0} \frac{\cos x\cos\Delta x - \sin x\sin\Delta x - \cos x}{\Delta x}\\
& = & \lim_{\Delta x \rightarrow 0} \frac{\cos x(\cos\Delta x - 1) - \sin x\sin\Delta x}{\Delta x}\\
- & = & \cos x\lim_{\Delta x \rightarrow 0}\frac{\cos\Delta x - 1}{\Delta x}
+ & = & \cos x\lim_{\Delta x \rightarrow 0}\frac{\cos\Delta x - 1}{\Delta x}
- \sin x\lim_{\Delta x \rightarrow 0}\frac{\sin\Delta x}{\Delta x}\\
& = & -1 \qquad\mbox{(using given results)}
\end{eqnarray*}}
-\endinput
-%%
-%% End of file `1stprncp.tex'.