Question

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

Answer 1

I've attached my question.

Answer 2

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.

Answer 3

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.

Answer 4

Yes, that's it.

Answer 5

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

Answer 6

I think so, yeah.