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Popular >

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

Solution

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

Solution

Period : π

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

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

Y Intercepts : (0, 1)

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

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

+1

Interval Notation

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

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

Solution steps

Periodicity of

tan (x) + sec^{2} (x) : π

Domain of

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

Range of

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

Axis interception points of

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

Y Intercepts

: (0, 1)

Asymptotes of

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

Vertical

: x = \frac{π}{2} + πn

Extreme Points of

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

Minimum

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

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Frequently Asked Questions (FAQ)

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