anonymous
  • anonymous
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?
OCW Scholar - Single Variable Calculus
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
phi
  • phi
if you have f(x) and g(x) both represented as a power series (i.e. increasing powers of x) then you can find the series representation of f(x)*g(x) by multiplying the two series. If you are only interested in a quadratic approximation, you would drop the "higher order" terms. We could use infinite series as an example, but let's just say both f(x) and g(x) are represented by a series up to x^8. You do the f(x)*g(x) multiplication, and collect the terms of the same power, and then at the end, drop all terms higher than x^2. You will see that you only needed to start with the terms up to x^2 in f(x) and g(x), and most of your work was wasted. In other words, if you only want a quadratic series for the product, you only need the terms up to x^2 in the multiplicands.
anonymous
  • anonymous
Thanks, that was quite helpful, although it doesn't address the case where f(x) and g(x) are not power series. It seems to me that there could be some crazy functions f and g that would not behave if you put them through the product rule prior to finding the quadratic approximation.

Looking for something else?

Not the answer you are looking for? Search for more explanations.