Absolute value of x divided by x

Asked by maham237 @ 22/02/2021 in Mathematics viewed by 279 People

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.

Answered by maham237 @ 22/02/2021

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

Absolute value of x divided by x

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