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Popular >

f(x)= 1/((1+sec(x))^2)

Solution

f (x) = \frac{1}{( 1 + sec ( x ) ) ^{2}}

Solution

Period : 2 π

Domain : 2 πn \leq 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) > 0

Y Intercepts : (0, \frac{1}{4})

Asymptotes : Vertical x = π + 2 πn

Extreme Points : None

+1

Interval 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 : (0, \infty)

Solution steps

Periodicity of

\frac{1}{( 1 + sec ( x ) ) ^{2}} : 2 π

Domain of

\frac{1}{( 1 + sec ( x ) ) ^{2}} : 2 πn \leq 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 of

\frac{1}{( 1 + sec ( x ) ) ^{2}} : f (x) > 0

Axis interception points of

\frac{1}{( 1 + sec ( x ) ) ^{2}} :

Y Intercepts

: (0, \frac{1}{4})

Asymptotes of

\frac{1}{( 1 + sec ( x ) ) ^{2}} :

Vertical

: x = π + 2 πn

Extreme Points of

\frac{1}{( 1 + sec ( x ) ) ^{2}} :

None

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Frequently Asked Questions (FAQ)

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