Thread: Beginners calculus type of question (...I think)

Hi. I answered this question but I have no idea if I did it correctly...

Question: Find a that fulfills: if , then

Answer: =

That part was easy, now is the part I don't know if I did logically/correctly...

The function is not defined at so we can require (so the x can stay away from )

so that

So now we get



and since ,

Therefore if we require , we will for sure get for



and so

Thanks!

**edit thanks for your advice!

You were doing great until the very end. This line:
5|x+1| < \delta < \frac{1}{100}, should be
5|x+1| < 5\delta < \frac{1}{100}. You corrected it in the next line, though.
Also, you found that delta < 1/500. Great! Stop right there. You're done. delta < 1/5 does NOT satisfy the requirement.

Originally Posted by Ackbeet

You were doing great until the very end. This line:
5|x+1| < \delta < \frac{1}{100}, should be
5|x+1| < 5\delta < \frac{1}{100}. You corrected it in the next line, though.

Thanks! That was a typo. I'll edit it.

Also, you found that delta < 1/500. Great! Stop right there. You're done. delta < 1/5 does NOT satisfy the requirement

Thanks again. I just got confused since my initial statement was (1) but I guess since my final result was (2) , as long as I choose a number smaller than (2), it also satisfies (1)....(as long as it's bigger than 0...)

Looks like you're good to go, then. Yeah, you have to take the more restricted condition in cases like this.