1. ## Limits

So unfortunately, I missed one class and that was when we were learning about limits. The only thing I understand is that the limit does not exist if going towards an x value, the y value's are positive and negative.

So I understand that this:

would equal 1, right? (I hope, or I really need to get help with this stuff)

But I don't understand what I'm supposed to do with this:

Would it equal 2? it says x doesn't equal two... but does. I'm confused.

2. Originally Posted by forsheezy
So unfortunately, I missed one class and that was when we were learning about limits. The only thing I understand is that the limit does not exist if going towards an x value, the y value's are positive and negative.

So I understand that this:

would equal 1, right? (I hope, or I really need to get help with this stuff)

But I don't understand what I'm supposed to do with this:

Would it equal 2? it says x doesn't equal two... but does. I'm confused.

For the first one direct substitution of the limit yields a determinant form. Determinant form just means it has no problems like divide by zero etc.

So $\lim_{x\to{1}}x+2=(1)+2=3$

For the second one a limit is defined as the value as $x\to{c}$ what $f(x)\to$

So the exact value at x=2 is not equivalent to limit since f(x) is not continous at x=2

But $\lim_{x\to{c}}f(x)\text{ }\exists\text{ }\text{iff}\text{ }\lim_{x\to{c^{-}}}f(x)=\lim_{x\to{c^{+}}}f(x)$

And as it does $\lim_{x\to{2^{-}}}f(x)=4-(2)=2=\lim_{x\to{2^{+}}}f(x)$

$\therefore\lim_{x\to{2}}f(x)=2$

3. Thank You
I somewhat understand it now!