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

-1

Explanation:

Given,

`lim_(x\rightarrow 4^(-)) (|x-4|)/(x-4)`

Let h represents a small change,

So, we can write,

`lim_(x\rightarrow 4-h) (|x-4|)/(x-4)`

`=(|4-h-4|)/(4-h-4)`

`=(|-h|)/(-h)`

`=(h)/(-h)`

`=-1`

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