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

The limit as x approaches 1-of x/(ln(x)) is -infinity

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limit as x approaches 1-of x/(ln(x))

x \to 1 - lim (\frac{x}{ln ( x )})

- \infty

Solution steps

x \to 1 - lim (\frac{x}{ln ( x )})

\frac{x}{ln ( x )} = x \frac{1}{ln ( x )}

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

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

With the exception of indeterminate form

= x \to 1 - lim (x) \cdot x \to 1 - lim (\frac{1}{ln ( x )})

x \to 1 - lim (x) = 1

x \to 1 - lim (\frac{1}{ln ( x )}) = - \infty

= 1 \cdot (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

\int sin (x^{3} + 1) d x

\int \frac{( x + 3 )}{2 x ^{3} - 8 x} d x

\frac{\partial}{\partial y} (x e^{z})

f (x) = 6 - 6 x

\frac{d}{d x} (r^{2} - x^{2})

What is the limit as x approaches 1-of x/(ln(x)) ?
The limit as x approaches 1-of x/(ln(x)) is -infinity