f(x)=sin(x)+cos(2x)+sec(3x)

Solução

f (x) = sin (x) + cos (2 x) + sec (3 x)

Period : 2 π

Domain : 2 πn \leq x < \frac{π}{6} + 2 πn or \frac{π}{6} + 2 πn < x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{5 π}{6} + 2 πn or \frac{5 π}{6} + 2 πn < x < \frac{7 π}{6} + 2 πn or \frac{7 π}{6} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < \frac{11 π}{6} + 2 πn or \frac{11 π}{6} + 2 πn < x < 2 π + 2 πn

Y intersepta : (0, 2)

Asymptotes : Vertical x = \frac{11 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn, x = \frac{π}{6} + 2 πn

Notação de intervalo

Domain : [2 πn, \frac{π}{6} + 2 πn) \cup (\frac{π}{6} + 2 πn, \frac{π}{2} + 2 πn) \cup (\frac{π}{2} + 2 πn, \frac{5 π}{6} + 2 πn) \cup (\frac{5 π}{6} + 2 πn, \frac{7 π}{6} + 2 πn) \cup (\frac{7 π}{6} + 2 πn, \frac{3 π}{2} + 2 πn) \cup (\frac{3 π}{2} + 2 πn, \frac{11 π}{6} + 2 πn) \cup (\frac{11 π}{6} + 2 πn, 2 π + 2 πn)

Passos da solução

Periodicidade de

sin (x) + cos (2 x) + sec (3 x) : 2 π

Domínio de

sin (x) + cos (2 x) + sec (3 x) : 2 πn \leq x < \frac{π}{6} + 2 πn or \frac{π}{6} + 2 πn < x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{5 π}{6} + 2 πn or \frac{5 π}{6} + 2 πn < x < \frac{7 π}{6} + 2 πn or \frac{7 π}{6} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < \frac{11 π}{6} + 2 πn or \frac{11 π}{6} + 2 πn < x < 2 π + 2 πn

Pontos de intersecção com o eixo de

sin (x) + cos (2 x) + sec (3 x) :

Y intersepta

: (0, 2)

Assíntotas de

sin (x) + cos (2 x) + sec (3 x) :

Vertical

: x = \frac{11 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn, x = \frac{π}{6} + 2 πn

f (x) = lo g_{2} (- x) - 2

y = \frac{3 x - 6}{2}

f (x) = x^{2} - 4 x + 13

f (x) = \frac{3 x ^{2} - 24 x - 99}{∣ 11 - x ∣}

f (x) = \frac{sin ( x ) + cos ( x )}{cos ( 2 x )}