{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

mth.122.handout.11

mth.122.handout.11 - MTH 122 Calculus II Essex County...

This preview shows pages 1–2. Sign up to view the full content.

MTH 122 — Calculus II Essex County College — Division of Mathematics and Physics 1 Lecture Notes #11 — Sakai Web Project Material 1 Approximating Functions with Polynomials This particular sheet is based on an extra credit problem that I gave my MTH-121 students. It is based on taking derivatives and then fitting points to a particular polynomial, even though the differentiated function was not a polynomial. The basis of the project was to use increasing degree polynomials to approximate functions that have no obvious relationship to polynomials. For example the sine function near the origin can be approximated with an ever increasing degree polynomial of the form: sin x = x - x 3 3! + x 5 5! - x 7 7! + x 9 9! - x 11 11! + · · · Let’s take a look, and I’d like you to label the curves directly on the graph. Yes, they’re related to the sine function and the expansion above. One curve is the sine function, then a sequence of polynomials of degree 1, 3, 5, 7, 9 and 11. Take a look, it’s really amazing to see how this sequence proceeds. 0 Figure 1: Sine and a sequence of polynomial functions. Seven graphs in all.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern