Question

What is the right-hand limit of as x approaches f(x) = x/x-5 as x approaches 5?

Answer 1

Answer:

$+\infty$

Step-by-step explanation:

The expression for the right hand limit of f(x) is:

$f = \frac{x+\epsilon}{x + \epsilon - 5}$

The expression can be simplified with some algebraic handling:

$f = \frac{1}{\frac{x+\epsilon-5}{x+\epsilon} }$

$f = \frac{1}{1-\frac{5}{x+\epsilon} }$

Let be $x = 5$, as $\epsilon$ is approaching zero, $f$ is positive and becomes bigger, diverging to $+\infty$.