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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.

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 class=

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apologiabiology
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:

-1

Step-by-step explanation:

Given,

[tex]lim_{x\rightarrow 4^{-}} \frac{|x-4|}{x-4}[/tex]

Let h represents a small change,

So, we can write,

[tex]lim_{x\rightarrow 4-h} \frac{|x-4|}{x-4}[/tex]

[tex]=\frac{|4-h-4|}{4-h-4}[/tex]

[tex]=\frac{|-h|}{-h}[/tex]

[tex]=\frac{h}{-h}[/tex]

[tex]=-1[/tex]

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

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