## anonymous 3 years ago Any idea how I can ask a question longer than 600 chars? I typed up a longish question that cannot be shortened.

1. anonymous

I've attached my question.

2. anonymous

For big questions, you could ask each part in a separate post. The equations in your attached question seem to be incorrect. For example, you've got "f(x) = x^2 + x/x+1" but the notes have$f(x)=\frac{x^{2}+x}{x+1}.$What you probably meant was f(x) = (x^2 + x)/(x+1), which would be the same as the notes. It's a good idea to use the equation button if you want to include equations. You asked, "Am I right in understanding that there's nothing inherently "easy" about calculating the limit of this function, but that it's only because we are looking for the limit as x tends to 3 that it becomes easy? In other words, if we wanted the limit as x approached zero then it would be a hard one?" No, you've not understood correctly. The case where x tends to zero is just as easy. It's only when x tends to -1 that it's hard in that particular example. For your second question, I think the notes have failed to say that$\Delta x=x-x_{0}.$I hope that clears up the confusion.

3. anonymous

Thanks for your response. I think I see it now. You're saying that $x_0$ cannot be equal to $x$ because then $\Delta x$ is equal to zero and we cannot divide by zero.

4. anonymous

Yes, that's it.

5. anonymous

So essentially, the example of $x \rightarrow x_0$ is the same thing as $\Delta x \rightarrow 0$?

6. anonymous

I think so, yeah.