Question

I can calculate this limit using L'hopitals, but the question also asks me to verify that the limit exists? What is it asking me to do to verify this?

Answer 1

What is the question?

Answer 2

\[\lim_{x \rightarrow 0}((1+x/2)\log(1+x)-x)/x^3\]

Answer 3

Sorry, I just wanted to put it properly :P

Answer 4

well, the only thing that pops up in my head is to show that the limit exists with epsilon delta definition...

Answer 5

Ah okay, I shall give that a go tomorrow, will I be okay to message you if I struggle with this?

Answer 6

You may want to verify with your teacher just what the question means. I'm pretty sure using epsilon delta to verify it would be kinda overkill.

Answer 7

Also, to be honest, I never really went over epsilon delta. I could lok over the problem if your teacher did in fact say he/she wanted that though.

Answer 8

Okay that's cool :) yeah I know what you mean about overkill. Maybe I could just show that the function satisfies the criteria for l'hopitals?
But thanks, I shall search for some clarification (:

Answer 9

yeah. perhaps that is what they want xD