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# Cálculo I

DisciplinaCálculo II33.949 materiais884.215 seguidores
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```1

Se o
lim\u210e\u21920
\ud835\udc53 \ud835\udc65+\u210e \u2212\ud835\udc53 \ud835\udc65
\u210e

não existe ou é
infinito, a função não
é derivável.
\ud835\udc25\ud835\udc22\ud835\udc26
\ud835\udc99\u2192\ud835\udc82
\ud835\udc84.\ud835\udc87 \ud835\udc99 = \ud835\udc84. \ud835\udc25\ud835\udc22\ud835\udc26
\ud835\udc99\u2192\ud835\udc82
\ud835\udc87 \ud835\udc99
\ud835\udc25\ud835\udc22\ud835\udc26
\ud835\udc99\u2192\ud835\udc82
\ud835\udc84 = \ud835\udc84
Dados \ud835\udc25\ud835\udc22\ud835\udc26\ud835\udc99\u2192\ud835\udc82 \ud835\udc87 \ud835\udc99 , \ud835\udc25\ud835\udc22\ud835\udc26\ud835\udc99\u2192\ud835\udc82 \ud835\udc88 \ud835\udc99 , c=cte,

lim
\ud835\udc65\u2192\u221e
1 +
1
\ud835\udc65
\ud835\udc65 = \ud835\udc52
lim
\ud835\udc65\u21920
\ud835\udc60\ud835\udc52\ud835\udc5b \ud835\udc65
\ud835\udc65 = 1
Limites Fundamentais

Tabela de Integrais

1. \ud835\udc50 \ud835\udc51\ud835\udc65 = \ud835\udc50\ud835\udc65 + \ud835\udc58
2. \ud835\udc65\ud835\udefc \ud835\udc51\ud835\udc65 =
\ud835\udc65\ud835\udefc+1
\ud835\udefc+1
+ \ud835\udc50 \ud835\udefc \u2260 \u22121
3.
1
\ud835\udc65
\ud835\udc51\ud835\udc65 = ln \ud835\udc65 + \ud835\udc50
4. \ud835\udc52\ud835\udc65\ud835\udc51\ud835\udc65 = \ud835\udc52\ud835\udc65 + \ud835\udc50
5. \ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udc65 \ud835\udc51\ud835\udc65 = \ud835\udc60\ud835\udc52\ud835\udc5b \ud835\udc65 + \ud835\udc50
6. \ud835\udc60\ud835\udc52\ud835\udc5b\ud835\udc65 \ud835\udc51\ud835\udc65 = \u2212\ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udc65 + \ud835\udc50
7. \ud835\udc60\ud835\udc52\ud835\udc502\ud835\udc65 \ud835\udc51\ud835\udc65 = \ud835\udc61\ud835\udc54\ud835\udc65 + \ud835\udc50
8. \ud835\udc60\ud835\udc52\ud835\udc50\ud835\udc65 \ud835\udc61\ud835\udc54\ud835\udc65 \ud835\udc51\ud835\udc65 = \ud835\udc60\ud835\udc52\ud835\udc50\ud835\udc65 + \ud835\udc50
9. \ud835\udc60\ud835\udc52\ud835\udc50\ud835\udc65 \ud835\udc51\ud835\udc65 = ln \ud835\udc60\ud835\udc52\ud835\udc50\ud835\udc65 + \ud835\udc61\ud835\udc54\ud835\udc65 + \ud835\udc50
10. \ud835\udc61\ud835\udc54\ud835\udc65 \ud835\udc51\ud835\udc65 = \u2212 ln \ud835\udc50\ud835\udc5c\ud835\udc60\ud835\udc65 + \ud835\udc50
11.
1
1+\ud835\udc652
\ud835\udc51\ud835\udc65 = \ud835\udc4e\ud835\udc5f\ud835\udc50\ud835\udc61\ud835\udc54\ud835\udc65 + \ud835\udc50
12.
1
1\u2212\ud835\udc652
\ud835\udc51\ud835\udc65 = \ud835\udc4e\ud835\udc5f\ud835\udc50\ud835\udc60\ud835\udc52\ud835\udc5b\ud835\udc65 + \ud835\udc50

1. \ud835\udc53 \ud835\udc65 + \ud835\udc54 \ud835\udc65 \ud835\udc51\ud835\udc65 = \ud835\udc53 \ud835\udc65 \ud835\udc51\ud835\udc65 + \ud835\udc54 \ud835\udc65 \ud835\udc51\ud835\udc65
2. \ud835\udc50\ud835\udc53 \ud835\udc65 \ud835\udc51\ud835\udc65 = \ud835\udc50 \ud835\udc53 \ud835\udc65 \ud835\udc51\ud835\udc65 (c=cte)

\uf0b7 f(x)=k \uf0e0 f\u2019(x)=0
\uf0b7 f(x)=x\u3b1 \uf0e0 f\u2019(x)=\u3b1.x\u3b1-1
\uf0b7 f(x)=ex \uf0e0 f\u2019(x)=ex
\uf0b7 f(x)=ln x \uf0e0 f\u2019(x)=1/x
\uf0b7 f(x)=sen x \uf0e0 f\u2019(x)=cos x
\uf0b7 f(x)=cos x \uf0e0 f\u2019(x)=-sen x
\uf0b7 f(x)=tg x \uf0e0 f\u2019(x)=sec2 x
\uf0b7 f(x)=sec x \uf0e0 f\u2019(x)=sec x tg x
\uf0b7 f(x)=cotg x \uf0e0 f\u2019(x)=-cosec2x
\uf0b7 f(x)=cosec x \uf0e0 f\u2019(x)=-cosec x cotg x

Regras de Derivação

\uf0b7 (f+g)\u2019=f\u2019(p)+g\u2019(p)
\uf0b7 (kf)\u2019(p)=kf\u2019(p)
\uf0b7 (f.g)\u2019(p)=f\u2019(p)g(p)+f(p)g\u2019(p)
\uf0b7 (f/g)\u2019(p)=f\u2019(p)g(p)-f(p)g\u2019(p)/(g(p))²

\uf0b7 Regra da Cadeia \u2013 (f o
g)\u2019(x)=f\u2019(g(x)).g\u2019(x)

\uf0b7 f derivável=f contínua```