Find the Limits: Testing the Boundaries

[PistonsMVP]

Find the Limits1. lim 312
x->11+

2. lim (x^2 +9)/(x^2 -1)
x->1for #2 i got 10 as the answer, but I'm not sure if its right. Thanks

edit: Sorry, wrong forum

 

[phreak]

1) do you know what a limit is? if so, looking at the behavior of the function should hint you as to what the answer is.

2) 10 isn't the correct answer. many people confuse the answers of 0/0 and x/0 or 0/x. The former gives odd results, whereas the latter two produce the same result, no matter what x is.

 

[courtrigrad]

phreak what do you mean by "the former gives odd results?"PistonsMVP, the limit of a contant function is what?

 

[PistonsMVP]

nm i figured it out. #1 is 312
and #2 DNE because 10/0

 

[Gib Z]

excuse me...isnt the point of a limit to find what value it approaches and not complain that its undefined?

btw the 2nd limit is -infinity

 

[d_leet]

excuse me...isnt the point of a limit to find what value it approaches and not complain that its undefined?

o btw the 2nd limit is -5

How is it -5?

 

[radou]

How is it -5?

It is not -5. And there is a big difference between 10/0, which is undefined, and the limit of the function as x -> 1.

 

[HallsofIvy]

excuse me...isnt the point of a limit to find what value it approaches and not complain that its undefined?

btw the 2nd limit is -infinity

Saying that the limit is -infinity is just a way of saying that it is not defined. Saying that a limit is undefine is not "complaining", it is stating a fact.

 

[dontdisturbmycircles]

$$\lim_{x \to a} f(x) = +\infty$$ or $$\lim_{x \to a} f(x) = -\infty$$

Just describes HOW a limit is not defined (whether it can be made arbitrarily large positive/large negative as x->a), but it definitely is not defined!