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

Apply Infinity Property:

c - \infty = - \infty

= - \infty

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