limit as x approaches 0 of x-1/(ln|x|)

Let's evaluate the limit of

x - \frac{1}{\ln | x |}

when

x \to 0

ⓘ The function abs is continuous, its limit is its value at the limit of its argument

The limit of

| x |

0

⁺ when

x \to 0

ⓘ This is a reference limit of the function ln

The limit of

\ln | x |

-∞

when

x \to 0

ⓘ A number divided by a quantity that grows without bound tends to 0

The limit of

- \frac{1}{\ln | x |}

0

⁺ when

x \to 0

ⓘ The limit of a sum of finite limits is the sum of the limits

So the limit of

x - \frac{1}{\ln | x |}

0

⁺ when

x \to 0

▶Limit:

0