Cálculo I
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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 
 
Propriedades da Integral 
 
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) 
 
Tabela de Derivados 
 
\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