What is the f(x)= 1/(xln(x)) ?

f(x)= 1/(xln(x))

f (x) = \frac{1}{x ln ( x )}

Domain : 0 < x < 1 or x > 1

Range : f (x) \leq - e or f (x) > 0

Intercepts : None

Asymptotes : Vertical x = 0, x = 1, Horizontal y = 0

Extreme Points : Maximum (\frac{1}{e}, - e)

Interval Notation

Domain : (0, 1) \cup (1, \infty)

Range : (- \infty, - e] \cup (0, \infty)

Solution steps

Domain of

\frac{1}{x ln ( x )} : 0 < x < 1 or x > 1

Range of

\frac{1}{x ln ( x )} : f (x) \leq - e or f (x) > 0

Axis interception points of

\frac{1}{x ln ( x )} :

None

Asymptotes of

\frac{1}{x ln ( x )} :

Vertical

: x = 0, x = 1,

Horizontal

: y = 0

Extreme Points of

\frac{1}{x ln ( x )} :

Maximum

(\frac{1}{e}, - e)

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\int_{1}^{2} 21 x^{2} 4^{x^{3}} d x