Question

limit of x as it approaches 2 from the right when 1/(x-2)

Answer 1

there is either "no limit" or you might be asked to say positive infinity, depending on the teacher

Answer 2

x approaches 2 from the right means x is larger than 2 (but getting close to 2) and so \(x-2\) is positive
then as the denominator gets closer and closer to 0 through positive numbers, the fraction gets larger and larger

Answer 3

you can see the horizontal asymptote at \(x=2\) and you can see that if you approach 2 from the right you are headed right up to infinity
http://www.wolframalpha.com/input/?i=1%2F%28x-2%29

Answer 4

sorry, my computer just glitched and I just saw this

Answer 5

the book says it's positive infinity

Answer 6

I was wondering how it got to infinity, thank you! in reality though it does not exsist though right?

Answer 7

You're basically starting by plugging in values of x that are larger than x = 2

Then you are slowly getting closer and closer to x = 2

Answer 8

So plug in x = 2.5 for instance to get y = 2

Then plug in x = 2.25 to get y = 4

Plug in x = 2.125 to get y = 8

etc etc

You'll see that as you get closer and closer to x = 2 from the right, y will approach positive infinity

Answer 9

thank you!

Answer 10

you're welcome