Question

HELPP!!
Select the correct answer.
What is the left-hand limit of as x approaches 4?

Answer 1

`\displaystyle\\\lim_(x\to4^-)(|x-4|)/(x-4)=\lim_(x\to4^-)(-(x-4))/(x-4)=\lim_(x\to4^-)-1=-1`

Answer 2

-1

Explanation:

|x-4|=x-4 when x-4 is positive or zero.

|x-4|=-(x-4) when x-4 is negative or zero.

x-4 is positive or zero means:

x-4>=0

Add 4 on both sides gives:

x>=4

x-4 is negative or zero means:

x-4<=0

Add 4 on both sides gives:

x<=4

Now we are approaching values of 4 from the left which means these values are less than 4 which makes x-4 negative.

So we are using:

|x-4|=-(x-4) when x-4 is negative or zero.

As x approaches 4 from left we have:

|x-4|/(x-4)=-(x-4)/(x-4)=-1.