What is the limit as x approaches 0+of (ln(x))/(1/x) ?

The limit as x approaches 0+of (ln(x))/(1/x) is 0

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limit as x approaches 0+of (ln(x))/(1/x)

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

0

Solution steps

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

Simplify

= 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

f (x) = x^{3} - 3 x - 5, at x = 1

\frac{\partial}{\partial x} (ln (x + 6 y + 8 z))

\frac{d y}{d x} = - \frac{2}{x ^{3}} + 2 e^{2 x - 2}

f (x) = 2 x^{2} + 5 x^{2} - 2, at x = 2

y = x^{2} + 6

What is the limit as x approaches 0+of (ln(x))/(1/x) ?
The limit as x approaches 0+of (ln(x))/(1/x) is 0