Learning Calculus BC had been a somewhat predictable process of applying rules and formulas, until I met Taylor series. A quirky combination of X, N, derivatives, and factorials, it overwhelmed me with such a bombastic look. Yes, I heard of its annual domination of the last question in free response. Yes, I did see a repeating pattern in it, but what exactly is Taylor series and how do those fancy concepts such as LagrangeError Bound relate to it? The mystery of Taylor series engaged me so deeply that I had turned myself into an ambitious detector searching for any possible clue. I divided my task into two parts: extensive clue-searching and direct investigation.
High School Math : Understanding Taylor Series
Taylor and I | University of Virginia Undergraduate Application Essay | GradeSaver
Your body has a strange property: you can learn information about the entire organism from a single cell. Pick a cell, dive into the nucleus, and extract the DNA. You can now regrow the entire creature from that tiny sample. There's a math analogy here. Take a function, pick a specific point, and dive in. You can pull out enough data from a single point to rebuild the entire function. It's like remaking a movie from a single frame.
Give the term of the Maclaurin series of the function. The term of the Maclaurin series of a function has coefficient. The second derivative of can be found as follows:. The coeficient of in the Maclaurin series is therefore. Give the term of the Taylor series expansion of the function about.
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