Absolute values often show up in problems involving square roots. That’s because you can’t take the square root of a negative number without introducing imaginary numbers (those involving $i = \sqrt{-1}$ ). Example 1: Simplify $\sqrt{x^{2}}$ This problem looks deceptively simple. Many students...

Absolute Value and Logarithms Absolute values often turn up unexpectedly in problems involving logarithms. That’s because you can’t take the log of a negative number. Let’s first review the definition of the logarithm function: Logb x = y ⇔ by = x (The double arrow is a bi-conditional, which means...

L’Hospital’s Rule is a useful way to evaluate tricky limits. It is most often used for limits of indeterminate form. The rule is as follows: If $f(x)$ and $g(x)$ are differentiable on some interval around the number $a$ (or if $a=\infty$, $f(x)$ and $g(x)$ are differentiable for all...