Limits. Options

[annalucky]

Okay. I need help. There's a quiz tomorrow, and I have no clue on what's going on. I'm sure most of you guys are pretty good in math.

For each of the following, find the limit as X approaches infinity.

a] a(x)=1000/x

b] b(x)=x^3-1000x^2

c] c(x)=(3x^2 + 7x)/(x^2 + 1000)


How do we find the limit without a calculator?

any one want to explain how limits work?

Tips and tricks would be nice too.

[*RiC3xBoy*]

Just divide all values by the highest power of x and all values that are less than the highest are just zero.

a) 0
b) 1
c) 3


Here it is in more depth.
For example
b(x) = X^3 - 1000X^2. Now divide everything by the highest X power which is X^3.
So it is now X^3/X^3 - 1000X^2/X^3 and you get 1 - 1000/x. Everything that is like 1000/x or anything that has x on the denominator is assumed to be zero, but X is approaching infinity. The answer is now just 1.

[annalucky]

^ would it be the same for negative infinity?

[*RiC3xBoy*]

Dangit, I forgot sorry. I learned it first semester but RATS.

[*mipadi*]

Limits find a value that x approaches as x approaches a value. Basically, limits usually don't exist; their value is what x gets close to, but never quite reaches.

To analyze them, imagine what happens as x approaches the specified value—in this case, infinity. For example, your first function is a(x) = 1000/x. As x gets very large, what happens to 1000/x? It starts to get small, because a small number divided by a very large number is a tiny number. Furthermore, imagine x is infinity; anything divided by infinity is 0 (except for infinity divided by infinity), so lim(x -> infinity) of 1000/x is 0.

The others can be analyzed in the same way. In the second one, think about what happens as x approaches infinity. What is infinity cubed? What hapenes when you substract from that 1000 times infinity squared?

The same concept can, of course, be applied to the last one.