Question

Calculate the limit:
lim_{x rightarrow 2} \frac{x^2 + x + 1}{x^2 - 4}

Answer 1

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Answer 2

\[\lim_{x \rightarrow 2} \frac{x^2 + x + 1}{x^2 - 4}\]

Answer 3

Tends to infinity.

Answer 4

But why?

Answer 5

Because the bottom half tends to zero so you're dividing by a smaller and smaller number so the result of the division gets larger and larger.

Answer 6

jok. Think about this. If you take a number (in this case the numerator is 7) and divide it by a number that is getting closer and closer to zero. Try .0001 then .000001 then .000000001 And you can see they get arbitrarily large. That is to say, they tend to infinity. So the limit "technically" doesn't exist. But most people will accept saying it tends to infinity.

Answer 7

Wow. It was very obvious. Thanks!

Answer 8

No problem :)