Find the one-sided limit (if it exists). \lim_{x \rightarrow 2^+} ln(x^2 - 4)

Question:

Find the one-sided limit (if it exists).

$$\lim_{x \rightarrow 2^+} \ln(x^2 - 4) $$

Logarithm Function at the Origin:

The logarithmic function is defined for strictly positive values of its argument.

The logarithm function at the origin has a vertical asymptote, its limit on the right is equal to minus infinity.

Answer and Explanation:

Remembering how it behaves, the limit in zero of the logarithm function, {eq}\ln (0) = - \infty. {/eq}

Applying the value of the limit, we have:

{eq}\mathop {\lim }\limits_{x \to {2^ + }} \ln ({x^2} - 4) = \ln ({2^2} - 4) = \ln (0) = - \infty. {/eq}


Learn more about this topic:

Logarithmic Properties

from Math 101: College Algebra

Chapter 10 / Lesson 5
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