Error Bounds for Correlation Clustering Form

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- [Instructor] Estimating sine of 0.4 using a Maclaurin polynominal, what is the least degree of the polynominal that assures an error smaller than 0.001? So what are we talking about here? Well, we could take some function and estimate it with an nth degree Maclaurin polynomial, in fact, we could talk more generally about a Taylor polynominal, but let's just say this is an nth degree Maclaurin polynomial, but this isn't going to be a perfect approximation, there's going to be some error or some remainder. And so we could call this the remainder of that nth degree Maclaurin polynomial, and it's going to be dependent for any given x. Now if we want to use the specifics of this exact problem, we could phrase it this way. We want to say, look, if we're taking the sine of 0.4 this is going to be equal to our Maclaurin, our nth degree Maclaurin polynomial evaluated at 0.4 plus whatever the remainder is for that nth degree Maclaurin polynomial evaluated at 0.4, and what we really want to do