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Trying to solve an introductory practice problem in my numerical analysis book. Help is very appreciated

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Hi u/Babyinthehood_,

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Are they requiring epsilon-delta? My thought would be to L’Hospital the limit.
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Hey, I picked a book on numerical analysis, a class that I will be taking next semester, and tried to solve an introductory practice problem to sharpen up my epsilon-delta skills.

I am not sure how to prove that the limit for continuity exists and to find K. I thought about expanding it into a taylor series centered around 0, but decided not to.

I have never done an epsilon-delta proof that was this challenging, just the ones in the classic Calc 1 class.

Isn't this the type of epsilon-delta stuff that is taught in real analysis?

Please help

Answer is f(0) = 1/6    (And presumably k = 1/6 )

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