From e221f7b641e26a5cdacb63cf64db4b26c38edec7 Mon Sep 17 00:00:00 2001 From: Charlie Root Date: Mon, 30 Mar 2026 17:17:23 -0300 Subject: [PATCH] More on differential equations (and cosmetics). --- calculus.pdf | Bin 922081 -> 922112 bytes calculus.tex | 8 ++++---- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/calculus.pdf b/calculus.pdf index 6717db758ab45a149bc04e7ca5eea8a8d9c5326a..7c16cdbe59ac9adefbb0c7eddb3fe77ce69ffcca 100644 GIT binary patch delta 10515 zcmajgQ*fOPv#)j=?f+Q4wW^bABNc@QqD8_!T|irEH90pWIT%)? z=x$;+RB7n)Cshr6YVD9+#-XE#6|WYAdTve&L8 z9HdfRVYN@Mx~eipJydX9kP!l1m|CSPeIE#nm2s!_4p zcMQ?hfRs5>Uw|@(D1lYpH9~Y7-9Vz^;kbO*1c%wUm}2hVK;DE`*XUl^K6&u1{$} zm9%Ja!8p^d0=Dtqz(jgZSC*mm%ayUe+X%nW`(heRQNU17=G0qWF4r%GFvuszSeg7z4L0+2t4wu z=zKK)F&r62PV2CVW0y(Djn61!r1H0&GGMjnKw)E z+U!f_W5eww$*3hC<_Ni~Pc=8z2%hkQ_*bP;U1OY$PAy4@?_EfjAj5ftE*|U;)DZ*_ zYWZ3+fO1YlMo@j|fgRgc=qNkzT|Rx0jiBpkWHqFlR+fZ-8=d<+r{V5e>_nDO+E(6t zsk(+4?q&t3&yC5R*YW0Vy<>k{{q`~^Pb2G{DKnGV@ZuJteK~LF^LpUA9WU#bV71-l 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nearby $x = a.$ -\subsection{Sobre a palavra ``tangente''} +\subsection{Sobre as palavras ``tangente'' e ``secante''} A linearização de uma curva, o que analisamos na Seção~\ref{sec:linearization}, é a obtenção de uma reta tangente a uma -curva $f(x)$. O nome ``tangente'' é usado primeiramente +curva $f(x)$. O nome ``tangente'' é usado primeiramente em trigonometria. Por que a palavra ``tangente'' reaparece na linearização local de uma curva? A palavra vem do Latim {\em tangens} que significa tocar. Usando o círculo unitário, desenhe um ângulo @@ -2999,8 +2999,8 @@ Quando computamos uma aproximação da inclinação da reta tangente, fazemos referência a retas ``secantes''. O termo ``secante'' vem do Latim ``secans'', que significa cortar. No círculo unitário, a reta secante corta o círculo. Ao estimarmos a inclinação de uma reta -tangente a uma curva, uma secante tende toca a curva em dois pontos, -ou seja, corta um pedaço da curva. +tangente a uma curva, uma secante toca a curva em dois pontos, ou +seja, corta um pedaço da curva. Veja também a Seção~\ref{sec:sine-cosine} pra compreender o ``co'' em ``cosseno''.