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Lynna [10]
3 years ago
15

HELP PLEASEE !!! What is the left-hand limit of f(x)=|x-3|/x-3 as approaches 3?

Mathematics
2 answers:
aleksklad [387]3 years ago
6 0

Answer:

-1

Step-by-step explanation:

x-3 is negative when x aproaches 3 from the left so the limit can be rewritten as

\lim_{x \to 3-} \frac{-x+3}{x-3}\\ = \lim_{x \to 3-} \frac{-(x-3)}{x-3}\\\\=-1

ladessa [460]3 years ago
3 0

Answer:

Option D  -1

Step-by-step explanation:

Given : Function f(x)=\frac{|x-3|}{x-3}

To find : What is the left-hand limit of function as approaches 3?      

Solution :

Function f(x)=\frac{|x-3|}{x-3}

In left-hand limit, x\rightarrow 3^-

x

So, f(x)=\frac{|x-3|}{x-3}=\frac{-(x-3)}{x-3}=-1,x\neq3

\lim_{x\rightarrow3^-}f(x)= \lim_{x\rightarrow3^-} (-1)=-1

Therefore, The left-hand limit of function as approaches 3 is -1.

So, Option D is correct.

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