College Math Placement Practice Test

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Question: 1 / 400

Evaluate the limit as x approaches 1 of (x² - 1)/(x - 1).

To evaluate the limit of the expression $(x^2 - 1)/(x - 1)$ as $x$ approaches 1, we can start by substituting $x = 1$ directly into the expression. However, doing so leads to an indeterminate form $0/0$, which necessitates further manipulation of the function to find the limit.

The expression $x^2 - 1$ can be factored using the difference of squares:

x^2 - 1 = (x - 1)(x + 1)

Thus, we can rewrite the original limit as:

\frac{(x - 1)(x + 1)}{x - 1}

As long as $x$ is not equal to 1, we can cancel out the $(x - 1)$ term from the numerator and the denominator:

x + 1

Now, we simply need to evaluate the limit of this new expression as $x$ approaches 1:

\lim_{x \to 1} (x + 1) = 1 + 1 = 2

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