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Popular Calculus >

f(x)=sin^3(3x)

Solution

f (x) = sin^{3} (3 x)

Solution

Period : \frac{2 π}{3}

Domain : - \infty < x < \infty

Range : - 1 \leq f (x) \leq 1

X Intercepts : (\frac{2 πn}{3}, 0), (\frac{π}{3} + \frac{2 πn}{3}, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Minimum (\frac{2 π}{3} n, 0), Maximum (\frac{π}{6} + \frac{2 π}{3} n, 1), Saddle (\frac{π}{3} + \frac{2 π}{3} n, 0), Minimum (\frac{π}{2} + \frac{2 π}{3} n, - 1)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 1, 1]

Solution steps

Periodicity of

sin^{3} (3 x) : \frac{2 π}{3}

Domain of

sin^{3} (3 x) : - \infty < x < \infty

Range of

sin^{3} (3 x) : - 1 \leq f (x) \leq 1

Axis interception points of

sin^{3} (3 x) :

X Intercepts

: (\frac{2 πn}{3}, 0), (\frac{π}{3} + \frac{2 πn}{3}, 0),

Y Intercepts

: (0, 0)

Asymptotes of

sin^{3} (3 x) :

None

Extreme Points of

sin^{3} (3 x) :

Minimum

(\frac{2 π}{3} n, 0),

Maximum

(\frac{π}{6} + \frac{2 π}{3} n, 1),

Saddle

(\frac{π}{3} + \frac{2 π}{3} n, 0),

Minimum

(\frac{π}{2} + \frac{2 π}{3} n, - 1)

Graph

Popular Examples

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\frac{d}{d x} (2 \cdot cos (x))

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\int x^{3} ln (x^{4}) d x

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\frac{d}{d x} (\frac{x ^{2} + 2 x - 2}{( x + 1 ) ^{2}})

Frequently Asked Questions (FAQ)

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