diff options
author | Karl Berry <karl@freefriends.org> | 2007-07-28 00:29:08 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2007-07-28 00:29:08 +0000 |
commit | 59e589a13e8de3ebc58828416bdd1eb4269b7bd2 (patch) | |
tree | 78564d8ec87320790f651149217dcb4d9eec7ea4 /Master/texmf-dist/doc/latex/probsoln/1stprncp.tex | |
parent | aea330a2bc712291777bdb4bf73fe68b594227ff (diff) |
probsoln 2.03 (18jul07)
git-svn-id: svn://tug.org/texlive/trunk@4672 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/probsoln/1stprncp.tex')
-rw-r--r-- | Master/texmf-dist/doc/latex/probsoln/1stprncp.tex | 36 |
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'. |