What is the limit as x approaches 0+of (x)(ln(x)) ?

The limit as x approaches 0+of (x)(ln(x)) is 0

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limit as x approaches 0+of (x)(ln(x))

x \to 0 + lim ((x) (ln (x)))

0

Solution steps

x \to 0 + lim (x ln (x))

Rewrite for L'Hopital

= x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x}})

Apply L'Hopital's Rule

: x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}})

= x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}})

Simplify

\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}} : - x

= x \to 0 + lim (- x)

Plug in the value

x = 0

= - 0

Simplify

= 0

x \to 0 + lim (ln (e^{x} - 1))

x \to + 0 lim (\frac{( cos ( m x ) - cos ( n x ) )}{x ^{2}})

x \to 0 lim (4 x - 8)

x \to \frac{1}{2} + lim (x^{2} tan (π x))

x \to - 1 lim (\frac{x}{∣ x + 1 ∣})

What is the limit as x approaches 0+of (x)(ln(x)) ?
The limit as x approaches 0+of (x)(ln(x)) is 0