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Popular >

h(t)= 1/3 sec^3(2t)-sec(2t)

Solution

h (t) = \frac{1}{3} sec^{3} (2 t) - sec (2 t)

Solution

Period : π

Domain : πn \leq t < \frac{π}{4} + πn or \frac{π}{4} + πn < t < \frac{3 π}{4} + πn or \frac{3 π}{4} + πn < t < π + πn

Range : - \infty < f (t) < \infty

X Intercepts : (\frac{arcsec ( - 3 )}{2} + πn, 0), (- \frac{arcsec ( - 3 )}{2} + π + πn, 0), (\frac{arcsec ( 3 )}{2} + πn, 0), (π - \frac{arcsec ( 3 )}{2} + πn, 0), Y Intercepts : (0, - \frac{2}{3})

Asymptotes : Vertical t = \frac{3 π}{4} + πn, t = \frac{π}{4} + πn

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

+1

Interval Notation

Domain : [πn, \frac{π}{4} + πn) \cup (\frac{π}{4} + πn, \frac{3 π}{4} + πn) \cup (\frac{3 π}{4} + πn, π + πn)

Range : (- \infty, \infty)

Solution steps

Periodicity of

\frac{1}{3} sec^{3} (2 t) - sec (2 t) : π

Domain of

\frac{1}{3} sec^{3} (2 t) - sec (2 t) : πn \leq t < \frac{π}{4} + πn or \frac{π}{4} + πn < t < \frac{3 π}{4} + πn or \frac{3 π}{4} + πn < t < π + πn

Range of

\frac{1}{3} sec^{3} (2 t) - sec (2 t) : - \infty < f (t) < \infty

Axis interception points of

\frac{1}{3} sec^{3} (2 t) - sec (2 t) :

X Intercepts

: (\frac{arcsec ( - 3 )}{2} + πn, 0), (- \frac{arcsec ( - 3 )}{2} + π + πn, 0), (\frac{arcsec ( 3 )}{2} + πn, 0), (π - \frac{arcsec ( 3 )}{2} + πn, 0),

Y Intercepts

: (0, - \frac{2}{3})

Asymptotes of

\frac{1}{3} sec^{3} (2 t) - sec (2 t) :

Vertical

: t = \frac{3 π}{4} + πn, t = \frac{π}{4} + πn

Extreme Points of

\frac{1}{3} sec^{3} (2 t) - sec (2 t) :

Minimum

(πn, - \frac{2}{3}),

Maximum

(\frac{π}{2} + πn, \frac{2}{3})

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