A function f(x) is said to have a jump discontinuity at x = a if:

A function f(x) is said to have a jump discontinuity at x = a if:

1. $\displaystyle{ \lim_{x\to a^-}f(x)}$ exists.

2. $\displaystyle{ \lim_{x\to a^+}f(x)}$ exists.

3. The left and right limits are not equal.

Let $f(x) = \begin{cases} 5 x - 2, &\text{if}\ x<10\\ \frac{4}{x+5}, &\text{if}\ x\geq 10 \end{cases}$

Show that f(x) has a jump discontinuity at x = 10 by calculating the limits from the left and right at x = 10.

$\displaystyle{ \lim_{x\to 10^-}f(x)}=$ ?

$\displaystyle{ \lim_{x\to 10^+}f(x)}=$ ?