The document contains 4 sections that provide formulas and properties for calculus and trigonometry: 1. Lists 12 derivative formulas including the derivatives of x^n, a^x, ln(x), sin(x), cos(x), tan(x), etc. 2. Lists 12 integral formulas including the integrals of x^n, ln(x), sin(ax), cos(ax), tan(x), sec(x), etc. 3. Provides 6 trigonometric formulas including formulas for sin(a+b), cos(a+b), sin^2(a), sin(2a), and cos(2a). 4. Lists 3 fundamental limits including the

1. 1
1 Tabela 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
2 Tabela de integrais
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 1
1+x2 dx = arctan x + C
1 H.C. http://math-ime-hc.blogspot.com.br/
https://www.slideshare.net/leinaddd88/
3 Fórmulas trigonométricas
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
cos a + cos b = cos
a + b
2
cos
a b
2
cos b cos a = 2 sin
a + b
2
sin
a b
2
4 Limites fundamentais
lim
x!0+
xx
= 1; lim
x!0
sin x
x
= 1; lim
x!+1
1 +
1
x
x
= e
1