I need some help with some calculus

assassinX

assassinX

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Um im having some trouble in Calculus, and I was wondering if anyone could help me with this problem,

lim r-->9 square root r/ (r-9)^4. I know the answer is infinity, but I dont know why and we can only use limits for this limit.

Also lim x-->8 approaching on the left side |x-8|/(x-8)

Any help would be appreciatve . :bouncy:
 
Just looking at them visually, The first function, as r approaches 9, sqrt r approaches 3. so the top is just the constant 3, then as the bottom approaches 9, it gets smaller and smaller. So, a number getting extremely close to 3 divided by a number that is getting extremely small equals an extremely big number, aka infinity.

The second one, as you plug in X values extremely close to 8, say, x= 7.99. You are going to have abs (7.99-8) = .01 . Now on the bottom, you are going to have 7.99-8 = -.01. Hence, the limit should approach -1. I could be wrong, but the lim of this from the right is 1, therefore, the limit from - does not equal limit from +, so lim of this wouldn't exist
 
I think afedrock already answered this pretty well.

On the second one, can you not have two limits? It's been a while since I took calculus, I would think the limits are +1 and -1. I don't remember only being able to have one limit or no limit exists.
 
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