Recall, is a continuous function.

So,

so the real problem is to find

Hint: You can use the squeeze theorem here.

Can you take it from here?

Recall the special limit:Second, this confused me, also..

Let f(x) = . Is the function f(x) continuous at x = 0? Can the function be extended to that it is continuous?

also recall,

Now, we note that:

since we have absolute values, we know that the can be negative or positive, depending on which direction we approach 0 from.Thus, when we see absolute values and we want the limit as we are approaching zero we must consider the one-sided limits.

So, exists if and only if and exists and are equal.

now find the limit.

why do we need to find the limit? they asked us about continuity.

i'm glad you asked. recall what it means for a function to be continuous at a certain point. (i'll give you the watered-down version).

A function is continuous at a point if:

Now continue...

I need to know how far you have reached with derivatives. do you have to use the limit definition, or can you do it the short way?Lastly..this one is just worded oddly..

Show that the line y = mx + b is its own tangent at any point

().

If any one could help me on any\all of this, I'd be very grateful ^_^ By the way, we haven't learned real derivatives yet so we have to do everything the long way in our work..