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

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

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

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

0

Solution steps

x \to 0 + lim (\frac{x}{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

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

x \to 0 + lim (x) = 0

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

= \frac{0}{- \infty}

Apply Infinity Property:

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

= 0

y^{^{''}} + 7 y^{^{'}} = 0, y (0) = 1, y^{^{'}} (0) = 1

\frac{d y}{d x} = 2 y x + y x^{2}, y (- 3) = 1

h (x) = \frac{1}{2 x}, at x = 4

x \to - 2 lim (2 x^{2})

\int x^{3} 5 + x^{2} d x

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