What is the limit as x approaches 0+of (2x)/(ln(x)) ?

The limit as x approaches 0+of (2x)/(ln(x)) is 0

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limit as x approaches 0+of (2x)/(ln(x))

x \to 0 + lim (\frac{2 x}{ln ( x )})

0

Solution steps

x \to 0 + lim (\frac{2 x}{ln ( x )})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 2 \cdot x \to 0 + lim (\frac{x}{ln ( x )})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= 2 \cdot \frac{lim _{x \to 0 +} ( x )}{lim _{x \to 0 +} ( ln ( x ) )}

x \to 0 + lim (x) = 0

x \to 0 + lim (ln (x)) = - \infty

= 2 \cdot \frac{0}{- \infty}

Simplify

2 \cdot \frac{0}{- \infty} : 0

= 0

\int \frac{cos ( x )}{cos ( x )} d x

8 x^{2} + x y + 8 y^{2} = 17, (1, 1)

y = 4 x^{3} - 12 x + 3

\int x^{2} - 5 x + 2 d x

(- 2.7) (- 3.4)

What is the limit as x approaches 0+of (2x)/(ln(x)) ?
The limit as x approaches 0+of (2x)/(ln(x)) is 0