In lecture 10, timestamped in this link:
https://www.youtube.com/watch?v=eRCN3daFCmU&t=21m13s
The prof is finding the quadratic approximation of a product of two functions. To find that, he simply takes the product of the quadratic approximations of the two functions.
My question is: how can we know that the product of two approximations is the approximation of a product? Is this guaranteed by some theorem somewhere?

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