Question

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

Answer 1

Answer:

-1

Step-by-step explanation:

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

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

Answer 2

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, $x\rightarrow 3^-$

$x<3\Rightarrow (x-3)<0\Rightarrow |x-3|=-(x-3)$

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.