Find the limit if it exists. If it doesn’t exist, explain why.

Question

thesmartone · Answer

$$\lim_{x \rightarrow 5^+}\frac{x-5}{|x-5|}$$

thesmartone · Answer

as it approaches from the right,

x is 5.01, 5.001, 5.0001

and it will be 0.01/0.01 = 0.001/0.001 = 0.0001/0.0001 = 1

So is the limit going to be 1?

thesmartone · Answer

The limit of the function as x appoaches 5 from the right will be 1.

If it approached from the left, it would be -1

And the limit of the function at 5 would be DNE 

mhmm

jsblumen · Answer

The 5+ means approaching from the right, so yes, the answer is 1. Because we are greater than 5, the absolute value means nothing because the bottom will always be postive when x>5. So then if you simplify the equation, you would get 1...just annother way to think about it than plug in numbers.

thesmartone · Answer

Thanks c: