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Popular Calculus >

f(x)=(cos(x))/(2+sin(x))

Solution

f (x) = \frac{cos ( x )}{2 + sin ( x )}

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - \frac{1}{3} \leq f (x) \leq \frac{1}{3}

X Intercepts : (\frac{π}{2} + 2 πn, 0), (\frac{3 π}{2} + 2 πn, 0), Y Intercepts : (0, \frac{1}{2})

Asymptotes : None

Extreme Points : Minimum (\frac{7 π}{6} + 2 πn, - \frac{1}{3}), Maximum (\frac{11 π}{6} + 2 πn, \frac{1}{3})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{1}{3}, \frac{1}{3}]

Solution steps

Periodicity of

\frac{cos ( x )}{2 + sin ( x )} : 2 π

Domain of

\frac{cos ( x )}{2 + sin ( x )} : - \infty < x < \infty

Range of

\frac{cos ( x )}{2 + sin ( x )} : - \frac{1}{3} \leq f (x) \leq \frac{1}{3}

Axis interception points of

\frac{cos ( x )}{2 + sin ( x )} :

X Intercepts

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

Y Intercepts

: (0, \frac{1}{2})

Asymptotes of

\frac{cos ( x )}{2 + sin ( x )} :

None

Extreme Points of

\frac{cos ( x )}{2 + sin ( x )} :

Minimum

(\frac{7 π}{6} + 2 πn, - \frac{1}{3}),

Maximum

(\frac{11 π}{6} + 2 πn, \frac{1}{3})

Graph

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n = 0 \sum \infty (\frac{5}{6})^{n}

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\frac{d}{d x} (x^{3} + 3 x^{2} + 1)

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\frac{\partial}{\partial x} (2 arctan (\frac{y}{x}))

Frequently Asked Questions (FAQ)

What is the f(x)=(cos(x))/(2+sin(x)) ?
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