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Popular >

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

Solution

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

Solution

Period : π

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

Range : f (x) \geq sec^{2} (- arctan (\frac{1}{2}) + π) - \frac{1}{2}

Y Intercepts : (0, 1)

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

Extreme Points : Minimum (- arctan (\frac{1}{2}) + π + πn, sec^{2} (- arctan (\frac{1}{2}) + π) - \frac{1}{2})

+1

Interval Notation

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

Range : [sec^{2} (- arctan (\frac{1}{2}) + π) - \frac{1}{2}, \infty)

Solution steps

Periodicity of

sec^{2} (x) + tan (x) : π

Domain of

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

Range of

sec^{2} (x) + tan (x) : f (x) \geq sec^{2} (- arctan (\frac{1}{2}) + π) - \frac{1}{2}

Axis interception points of

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

Y Intercepts

: (0, 1)

Asymptotes of

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

Vertical

: x = \frac{π}{2} + πn

Extreme Points of

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

Minimum

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

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Frequently Asked Questions (FAQ)

What is the f(x)=sec^2(x)+tan(x) ?
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