1. LIMIT ES FUNDAMENT AIS1
lim
x!0+
xx
= 1; lim
x!0
sin x
x
= 1; lim
x!+1
1 +
1
x
x
= e
T ABELA DE DERIVADAS
1. d
dx xn
= nxn 1
, n 6= 0
2. d
dx ax
= ax
ln a, (a > 0)
3. d
dx ln x = 1
x
4. d
dx sin x = cos x
5. d
dx cos x = sin x
6. d
dx tan x = sec2
x
7. d
dx cot x = sec2
x
8. d
dx sinh x = cosh x
9. d
dx cosh x = sinh x
10. d
dx arcsin x = 1p
1 x2
11. d
dx arccos x = 1p
1 x2
12. d
dx arctan x = 1
x2+1
T ABELA DE INT EGRAIS
1.
R
xn
dx = xn+1
n+1 + C, se n 6= 1
2.
R
ln x = x ln x x + C
3.
R 1
x dx = ln jxj + C
4.
R
sin axdx = 1
a cos ax + C, a 6= 0
5.
R
cos ax = 1
a sin ax + C
6.
R
tan xdx = ln (cos x) + C
7.
R
sinh xdx = cosh x + C
8.
R
cosh xdx = sinh x + C
9.
R
eax
dx = 1
a eax
+ C, a 6= 0
10.
R
sec xdx = ln jsec x + tan xj + C
11.
R 1
1 x2 dx = 1
2 ln x+1
x 1 + C
12.
R p
1 x2dx = 1
2 arcsin x + 1
2 x
p
1 x2 + C
13.
R 1p
1 x2
dx = arcsin x + C
14.
R 1p
x2 1
dx = arccosh x + C
15.
R 1p
1+x2
dx = arcsinh x + C
16.
R 1
1+x2 dx = arctan x + C
17.
R
arcsin xdx =
p
1 x2 + x arcsin x + C
18.
R
arccos xdx = x arccos x
p
1 x2 + C
19.
R
arctan xdx = x arctan x 1
2 ln x2
+ 1 + C
20.
R p
x2 1dx = 1
2 x
p
x2 1 1
2 ln x +
p
x2 1 + C
21.
R p
1 + x2dx = 1
2 ln x +
p
x2 + 1 + 1
2 x
p
x2 + 1 + C
22.
R
ex
sin xdx = 1
2 ex
(sin x cos x) + C
23.
R
ex
cos xdx = 1
2 ex
(cos x + sin x) + C
24.
R
sinn
xdx = 1
n sinn 1
x cos x + n 1
n
R
sinn 2
xdx
25.
R
cosn
xdx = 1
n cosn 1
x sin x + n 1
n
R
cosn 2
xdx
26.
R
tann
xdx = 1
n 1 tann 1
x
R
tann 2
xdx (n 6= 1)
FORMULAS T RIGONOMET RICAS
1. sin (a + b) = cos a sin b + cos b sin a;
2. cos (a + b) = cos a cos b sin a sin b
3. sin2 a
2 = 1 cos a
2 ; cos2 a
2 = 1+cos a
2
4. sin (2a) = 2 sin a cos a;
5. cos 2a = cos2
a sin2
a
6. sin a + sin b = 2 sin a+b
2 cos a b
2
7. cos a + cos b = cos a+b
2 cos a b
2
8. cos b cos a = 2 sin a+b
2 sin a b
2
1 H.C. http://math-ime-hc.blogspot.com.br/
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