Question

AP Calculus AB Summer Work help? (Limits)

Answer 1

how would you describe a limit?

Answer 2

A limit is a value something approaches.

That might be too simplified, but that's kinda what it is basically.

Answer 3

For the function f(x) = 1/x, what is the limit of f(x) as x--> infinity?

That's like asking what does f(x) approach as x approaches infinity?

Answer 4

If you look at the graph of y = 1/x, you would say that as x gets bigger and bigger (approaching infinity), the value of f(x) gets closer and closer to 0.

Answer 5

So the limit of f(x) as x approaches infinity, is 0.

Answer 6

Do you get it?

Answer 7

So like this:
Limit: the height a fan intends to reach. For any specific domain, there is a specific range value and the limit is that range value

Answer 8

oh! so the value that the function approaches as the domain approaches a certain value

Answer 9

Yes, what the function approaches as the domain approaches a certain value.

But remember this: the limit is not always the functional value at the specific domain. Sometimes the range value might not even exist, but the limit will exist.

Answer 10

awesome! thank u so much!

Answer 11

Here, I'll give you an example where the range value doesn't exist, but the limit does.

Answer 12

For the function\[f(x) = \frac {x^2 - 4}{x-2}\]At x = 2, the functional value is undefined, but if you were to graph this on a calculator, you would see that as x-->2, the function approaches 4.

Answer 13

oh i see! can u help me with a certain problem like this

Answer 14

just give me 5 minutes i have to go get my notes out

Answer 15

ok so umm

Answer 16

Some graphs are more mysterious, like