Question

please explain @ganeshie8

Answer 1

Now, here the limit of x approaches 4 from the left side.
So basically, the value should be = -1.

\[\lim_{x \rightarrow 4^-} \frac{|x-4|}{x-4} = -1\]

Answer 2

thanks!

Answer 3

to add to Akash

the \( x \rightarrow 4^-\) means x is less than 4 and approaches (but *never* reaches 4)
example 3.9 (to make it concrete)
| 3.9 - 4 | / (3.9- 4) = |-0.1|/ -0.1 = 0.1/-0.1 = -1
As x gets closer to 4 we can replace 0.1 with a *tiny* number \( \epsilon\)
\[ \frac{\epsilon}{- \epsilon} =-1 \]
the important idea is \( \epsilon \) is *never* allowed to be zero, so we can always divide to get -1