f(x)=(tan(x))^2+(cot(x))^2

Lösung

f (x) = (tan (x))^{2} + (cot (x))^{2}

Period : π

Domain : πn < x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

Range : f (x) \geq 2

Intercepts : Keine

Asymptotes : Vertikal x = \frac{π}{2} + πn, x = πn

Extreme Points : Minimum (\frac{π}{4} + πn, 2), Minimum (\frac{3 π}{4} + πn, 2)

Intervall-Notation

Domain : (πn, \frac{π}{2} + πn) \cup (\frac{π}{2} + πn, π + πn)

Range : [2, \infty)

Schritte zur Lösung

Periodizität von

tan^{2} (x) + cot^{2} (x) : π

Bereich von

tan^{2} (x) + cot^{2} (x) : πn < x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

Bereich von

tan^{2} (x) + cot^{2} (x) : f (x) \geq 2

Schnittpunkte mit der Achse von

tan^{2} (x) + cot^{2} (x) :

Keine

Asymptoten von

tan^{2} (x) + cot^{2} (x) :

Vertikal

: x = \frac{π}{2} + πn, x = πn

Extrempunkte vonf

tan^{2} (x) + cot^{2} (x) :

Minimum

(\frac{π}{4} + πn, 2),

Minimum

(\frac{3 π}{4} + πn, 2)

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