>>10981778I can't help you on your test. But I can help you conceptually.
Consider this: in real life whenever you're doing measurements, you will never be exactly right. There's always going to be some margin of error.
Let's take an example of 1/x
As you know, you can't divide by zero. But we can take the limit is x --> 0. That means we slide closer and closer to zero, until we get very close to it, and see what is happening to our function.
You can slide from the left, or slide from the right. Sometimes you will get different answers.
As you can see, as x gets closer and closer to zero, 1/x gets very large. In fact it goes to infinity.
Thus we can't say that 1/0 = infinity, but we can say that
Is that making sense?
You can do this at any point along a function, but you see how this can be useful at discontinuities.
Now consider a ratio like this:
As you march closer and closer to zero, the top will go to 7, and the bottom will go to 3. Thus when you get arbitrarily close to 0, the function should equal 7/3. Does that make sense?
Why is this thing with limits important?
Because sometimes you can have "dueling zeroes". So as you approach the limit, the top is going to zero, and the bottom is also going to zero. However, their ratio approaches a constant. So for example
We can also have "dueling infinities", where the top is trying to go to infinity, and the bottom is as well.
That's basically what you need to know about limits.
