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Popular >

f(x)=(cos(x))/(cos(x)+1)

Solution

f (x) = \frac{cos ( x )}{cos ( x ) + 1}

Solution

Period : 2 π

Domain : 2 πn \leq x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Range : f (x) \leq \frac{1}{2}

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

Asymptotes : Vertical x = π + 2 πn

Extreme Points : Maximum (2 πn, \frac{1}{2})

+1

Solution steps

Periodicity of

\frac{cos ( x )}{cos ( x ) + 1} : 2 π

Domain of

\frac{cos ( x )}{cos ( x ) + 1} : 2 πn \leq x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Range of

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

Axis interception points of

\frac{cos ( x )}{cos ( x ) + 1} :

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 )}{cos ( x ) + 1} :

Vertical

: x = π + 2 πn

Extreme Points of

\frac{cos ( x )}{cos ( x ) + 1} :

Maximum

(2 πn, \frac{1}{2})

Popular Examples

derivative of y=(6x)/(x^2+1)derivative of

y = \frac{6 x}{x ^{2} + 1}

integral of (1-sin(x))/(1-sin^2(x))

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

tangent of y=x^2+3,(-1,4)tangent of

y = x^{2} + 3, (- 1, 4)

integral from-4 to 4 of |x|

\int_{- 4}^{4} ∣ x ∣ d x

limit as x approaches-3 of (4x-5)/(3x+9)

x \to - 3 lim (\frac{4 x - 5}{3 x + 9})

Frequently Asked Questions (FAQ)

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