Question

Find limit as x approaches 4 from the left of the quotient of the absolute value of the quantity x minus 4, and the quantity x minus 4 . You must show your work or explain your work in words.
See below for the mathematical form of the equation.

Answer 1

This is fun

one way is to aproximate by getting values closer and closer to the value
the small negative sign on the top left of the 4 means we need to aproximate from the left, or from values less than 4 to 4

so like using 3.9, 3.99. 3.999, etc

if we did 3.9, we get 0.1/-0.1=-1
if we did 3.99, we get 0.01/-0.01=-1
if we did 3.999, we get 0.001/-0.001=-1
I notice a pattern

so therefor I say the limit as x approaches 4 from the left is -1

Answer 2

Answer:

-1

Step-by-step explanation:

Given,

$lim_{x\rightarrow 4^{-}} \frac{|x-4|}{x-4}$

Let h represents a small change,

So, we can write,

$lim_{x\rightarrow 4-h} \frac{|x-4|}{x-4}$

$=\frac{|4-h-4|}{4-h-4}$

$=\frac{|-h|}{-h}$

$=\frac{h}{-h}$

$=-1$

Hence, the value of the given limit is -1.