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Popular Calculus >

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

Solution

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

Solution

Period : π

Domain : πn < x < \frac{3 π}{4} + πn or \frac{3 π}{4} + πn < x < π + πn

Range : f (x) < 1 or f (x) > 1

X Intercepts : (\frac{π}{2} + πn, 0)

Asymptotes : Vertical x = \frac{3 π}{4} + πn

Extreme Points : None

+1

Interval Notation

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

Range : (- \infty, 1) \cup (1, \infty)

Solution steps

Periodicity of

\frac{cot ( x )}{1 + cot ( x )} : π

Domain of

\frac{cot ( x )}{1 + cot ( x )} : πn < x < \frac{3 π}{4} + πn or \frac{3 π}{4} + πn < x < π + πn

Range of

\frac{cot ( x )}{1 + cot ( x )} : f (x) < 1 or f (x) > 1

Axis interception points of

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

X Intercepts

: (\frac{π}{2} + πn, 0)

Asymptotes of

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

Vertical

: x = \frac{3 π}{4} + πn

Extreme Points of

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

None

Graph

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Frequently Asked Questions (FAQ)

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