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

The limit as x approaches 1-of 2/x-1/(ln(x)) is infinity

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limit as x approaches 1-of 2/x-1/(ln(x))

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

\infty

Solution steps

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

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

With the exception of indeterminate form

= x \to 1 - lim (\frac{2}{x}) - x \to 1 - lim (\frac{1}{ln ( x )})

x \to 1 - lim (\frac{2}{x}) = 2

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

= 2 - (- \infty)

Simplify

2 - (- \infty) : \infty

= \infty

\int \frac{- x + 2}{x ^{2} + 2 x + 4} d x

\frac{d y}{d x} = e^{- 2 y} tan^{2} (x)

x^{^{''}} + x^{^{'}} - 2 x = 0

y^{^{'}} = - \frac{y}{x}

x^{^{'''}} + x^{^{''}} + 3 x^{^{'}} - 5 x = 0

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