What is the limit as x approaches 0+of 2/(1+ln(x)) ?

The limit as x approaches 0+of 2/(1+ln(x)) is 0

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limit as x approaches 0+of 2/(1+ln(x))

x \to 0 + lim (\frac{2}{1 + ln ( x )})

0

Solution steps

x \to 0 + lim (\frac{2}{1 + 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{1}{1 + 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 +} ( 1 )}{lim _{x \to 0 +} ( 1 + ln ( x ) )}

x \to 0 + lim (1) = 1

x \to 0 + lim (1 + ln (x)) = - \infty

= 2 \cdot \frac{1}{- \infty}

Simplify

2 \cdot \frac{1}{- \infty} : 0

= 0

f (x) = x, at x = 2

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

sin (t) cos (t)

\frac{\partial}{\partial x} (5 x y e^{(x + y)})

What is the limit as x approaches 0+of 2/(1+ln(x)) ?
The limit as x approaches 0+of 2/(1+ln(x)) is 0