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Consider the piecewise function. f (x) = StartLayout Enlarged left-brace first row 2 x, x less-than 1 second row negative 4, x = 1 third row x + 8, x greater-than 1 EndLayout The function has a discontinuity at x = 1. What are Limit of f (x) as x approaches 1 minus and Limit of f (x) as x approaches 1 plus? Limit of f (x) = 2 as x approaches 1 minus. Limit of f (x) = 9 as x approaches 1 plus. Limit of f (x) = 9 as x approaches 1 minus. Limit of f (x) = 2 as x approaches 1 plus. Limit of f (x) = negative 4 as x approaches 1 minus. Limit of f (x) = negative 4 as x approaches 1 plus. Limit of f (x) D N E as x approaches 1 minus. Limit of f (x) D N E as x approaches 1 plus.

Sagot :

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Answer:

A) 2 9

Step-by-step explanation:

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Limit of f (x) = 2 as x approaches 1 minus. Limit of f (x) = 9 as x approaches 1 plus.

The correct option is (A)

What is piecewise function?

Piecewise function is a function built from pieces of different functions over different intervals.

The given function is: f(x)= [tex]\left \{ {{2x, \;\; x < 1} \atop {-4, \;\; x=1} \right \atop {x+8, \;\; x > 1}[/tex]

As,  piecewise function is a function built from pieces of different functions over different intervals.

As per the above discussion we can say that,

Take function for limit 1 minus, as f(x)  = 2x

put x=1,

f(x)=2, exits.

Take function for limit 1 plus, as f(x)  = x+8

put x=1,

f(x)=9, exits.

As both satisfies the definition and part (A)

As well as both limit exist and are not equal.

So, Limit of f (x) = 2 as x approaches 1 minus. Limit of f (x) = 9 as x approaches 1 plus for the given f(x).

Learn more about piecewise function here:

https://brainly.com/question/12561612

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