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Beliebt Funktionen >

f(x)=sec(x)csc^2(x)

Lösung

f (x) = sec (x) csc^{2} (x)

Lösung

Period : 2 π

Domain : 2 πn < x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < π + 2 πn or π + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Range : f (x) \leq - \frac{3 3}{2} or f (x) \geq \frac{3 3}{2}

Intercepts : Keine

Asymptotes : Vertikal x = 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn, x = π + 2 πn

Extreme Points : Minimum (arccot (\frac{1}{2}) + 2 πn, \frac{3 3}{2}), Maximum (arccot (- \frac{1}{2}) + 2 πn, - \frac{3 3}{2}), Maximum (arccot (\frac{1}{2}) + π + 2 πn, csc^{2} (arccot (\frac{1}{2}) + π) sec (arccot (\frac{1}{2}) + π)), Minimum (arccot (- \frac{1}{2}) + π + 2 πn, csc^{2} (arccot (- \frac{1}{2}) + π) sec (arccot (- \frac{1}{2}) + π))

+1

Intervall-Notation

Domain : (2 πn, \frac{π}{2} + 2 πn) \cup (\frac{π}{2} + 2 πn, π + 2 πn) \cup (π + 2 πn, \frac{3 π}{2} + 2 πn) \cup (\frac{3 π}{2} + 2 πn, 2 π + 2 πn)

Range : (- \infty, - \frac{3 3}{2}] \cup [\frac{3 3}{2}, \infty)

Schritte zur Lösung

Periodizität von

sec (x) csc^{2} (x) : 2 π

Bereich von

sec (x) csc^{2} (x) : 2 πn < x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < π + 2 πn or π + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Bereich von

sec (x) csc^{2} (x) : f (x) \leq - \frac{3 3}{2} or f (x) \geq \frac{3 3}{2}

Schnittpunkte mit der Achse von

sec (x) csc^{2} (x) :

Keine

Asymptoten von

sec (x) csc^{2} (x) :

Vertikal

: x = 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn, x = π + 2 πn

Extrempunkte vonf

sec (x) csc^{2} (x) :

Minimum

(arccot (\frac{1}{2}) + 2 πn, \frac{3 3}{2}),

Maximum

(arccot (- \frac{1}{2}) + 2 πn, - \frac{3 3}{2}),

Maximum

(arccot (\frac{1}{2}) + π + 2 πn, csc^{2} (arccot (\frac{1}{2}) + π) sec (arccot (\frac{1}{2}) + π)),

Minimum

(arccot (- \frac{1}{2}) + π + 2 πn, csc^{2} (arccot (- \frac{1}{2}) + π) sec (arccot (- \frac{1}{2}) + π))

Graph

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