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Popular >

f(x)=4sec(x)

Solution

f (x) = 4 sec (x)

Solution

Period : 2 π

Domain : 2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 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 - 4 or f (x) \geq 4

Y Intercepts : (0, 4)

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

Extreme Points : Minimum (2 πn, 4), Maximum (π + 2 πn, - 4)

+1

Interval Notation

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

Range : (- \infty, - 4] \cup [4, \infty)

Solution steps

Periodicity of

4 sec (x) : 2 π

Domain of

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

Range of

4 sec (x) : f (x) \leq - 4 or f (x) \geq 4

Axis interception points of

4 sec (x) :

Y Intercepts

: (0, 4)

Asymptotes of

4 sec (x) :

Vertical

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

Extreme Points of

4 sec (x) :

Minimum

(2 πn, 4),

Maximum

(π + 2 πn, - 4)

Popular Examples

(\partial)/(\partial x)(3sqrt(xy^2-2xy+z))

\frac{\partial}{\partial x} (3 x y^{2} - 2 x y + z)

y^{''}-4y^'+7y=0

y^{^{''}} - 4 y^{^{'}} + 7 y = 0

integral from-2 to 3 of (28)/(x^4)

\int_{- 2}^{3} \frac{28}{x ^{4}} d x

tangent of x^2=y^2,(1,-1)tangent of

x^{2} = y^{2}, (1, - 1)

tangent of f(x)=x^2-7x+7,\at x=0 tangent of

f (x) = x^{2} - 7 x + 7, at x = 0

Frequently Asked Questions (FAQ)

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