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Popular >

f(x)=csc^2(x)cos(2x)

Solution

f (x) = csc^{2} (x) cos (2 x)

Solution

Period : π

Domain : πn < x < π + πn

Range : f (x) \geq - 1

X Intercepts : (\frac{π}{4} + πn, 0), (\frac{3 π}{4} + πn, 0)

Asymptotes : Vertical x = πn

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

+1

Interval Notation

Domain : (πn, π + πn)

Range : [- 1, \infty)

Solution steps

Periodicity of

csc^{2} (x) cos (2 x) : π

Domain of

csc^{2} (x) cos (2 x) : πn < x < π + πn

Range of

csc^{2} (x) cos (2 x) : f (x) \geq - 1

Axis interception points of

csc^{2} (x) cos (2 x) :

X Intercepts

: (\frac{π}{4} + πn, 0), (\frac{3 π}{4} + πn, 0)

Asymptotes of

csc^{2} (x) cos (2 x) :

Vertical

: x = πn

Extreme Points of

csc^{2} (x) cos (2 x) :

Minimum

(\frac{π}{2} + πn, - 1)

Popular Examples

f(x)=arctan(x)+pi/2

f (x) = arctan (x) + \frac{π}{2}

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f (x) = (x^{3} - 2) e^{- 3 x - 5}

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f (x) = x^{2} + 4 x + 3

g(x)=(x+7)/(x^2-14x+49)

g (x) = \frac{x + 7}{x ^{2} - 14 x + 49}

f (x) = 6 x^{2} + 2 x - 1

Frequently Asked Questions (FAQ)

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