Another beginners calculus problem

Find an so that every fulfills

I've been brainstorming ideas, but it's a bit frustrating since I can't simplify the equation like I usually do.

Here are my thoughts and questions:

1) I'm thinking along the lines of proving something like because then I can simplify to . Is there any way I can make that happen?

2) Can ever be . Because if not, we know that must also be since the function must be .

3) Or can I just say M = 1000000000000, and since sinx is always between 1 and -1, it doesn't effect us, and 6x^2 is always bigger than 3x+1. so a x>M is definitely bigger than 1000.

Thanks!

You'd like a sequence of inequalities that look like this:



So, if you can make the expression smaller but still with a size that you can control, you're good.

Since you're subtracting the sin function, and you want your function to get smaller, make the term as big as possible:



Now work with this, and make it bigger than the desired amount.

Quote:

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Originally Posted by Ackbeet

You'd like a sequence of inequalities that look like this:



So, if you can make the expression smaller but still with a size that you can control, you're good.

Since you're subtracting the sin function, and you want your function to get smaller, make the term as big as possible:



Now work with this, and make it bigger than the desired amount.

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Thanks but I'm still stuck for some reason. Can you give me the next step?

I tried making but I got stuck. I tried taking away a 1 and a 7 but I'm not so sure what to do.

Hm...maybe I should simply solve for

and I should get x>(something). Then I can just make M=(something) so I know x is always >M

I think that procedure should work for you.