Calculus Examples

$lim_{x \to 1^{-}} \frac{\sqrt{2 \cdot x} (x - 1)}{| x - 1 |}$

Step 1

Make a table to show the behavior of the function $\frac{\sqrt{2 \cdot x} (x - 1)}{| x - 1 |}$ as $x$ approaches $1$ from the left.

$\begin{array}{c} x & \frac{\sqrt{2 \cdot x} (x - 1)}{| x - 1 |} \\ 0.9 & - 1.34164078 \\ 0.99 & - 1.40712472 \\ 0.999 & - 1.41350627 \\ 0.9999 & - 1.41414284 \end{array}$

Step 2

As the $x$ values approach $1$ , the function values approach $- 1.414$ . Thus, the limit of $\frac{\sqrt{2 \cdot x} (x - 1)}{| x - 1 |}$ as $x$ approaches $1$ from the left is $- 1.414$ .

$- 1.414$