I understand that the power rule for limits could be used here but my teacher wants it done using the epsilon delta definition.

1st attempt (though I think it's obviously wrong since my could be undefined):

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- Dec 14th 2011, 10:17 PMlamp23Prove limit of x^5 = a^5 using epsilon delta

I understand that the power rule for limits could be used here but my teacher wants it done using the epsilon delta definition.

1st attempt (though I think it's obviously wrong since my could be undefined):

- Dec 14th 2011, 10:26 PMChris11Re: Prove limit of x^5 = a^5 using epsilon delta
You're right that you need to factor. But, you shouldn't have x terms in your choice of delta. Try getting a bound on the big factor (x^4+...) by making a bound on x.

- Dec 14th 2011, 10:47 PMlamp23Re: Prove limit of x^5 = a^5 using epsilon delta
Do you mean something very similar to the below example?

Are you suggesting the bound I make is something like ?

which implies

http://oi39.tinypic.com/ambd6c.jpg - Dec 15th 2011, 12:36 PMChris11Re: Prove limit of x^5 = a^5 using epsilon delta
Indeed. But don't forget that you want an upper bound, and you certainly have that x< |a|+1 So, use this to get aqn upper bound on the big polynomial factor, take delta to be the minimum of 1 and epsilon/(bound on poly)