3 min readβ’june 7, 2020

Athena_Codes

We can use **power series** to approximate functions, which are called Taylor Series.

Once we know the formula for a power series, we can do several things to find other series, as we shall demonstrate from the following examples.

Using the Maclaurin Series above, find the sixth-order Maclaurin polynomial for the following functions.

Congratulations, youβre done with this unit, and as a result, youβve also reached the end of AP Calculus BC! Now, you have all the tools you need to ace that AP test this May!

Now, the question is, whatβs next after AP Calculus BC? If you are mainly interested in the humanities or want to go into research sciences, then AP Statistics is a great option. A lot of statistics is based off of calculus, even if the relationship isnβt explicitly stated.

Many science courses are also deeply rooted in calculus as well. AP Chemistry utilizes calculus indirectly with the concepts of reaction rates and rate laws. However, AP Physics C uses calculus freely and is a good challenge if you are interested in physics or want a little bit of a challenge!

If you want to go into higher STEM courses, then you may consider higher mathematical courses. However, there are some concepts in single-variable calculus that arenβt covered in AP Calculus that are useful for higher math courses such as hyperbolic functions, the epsilon-delta definition of a limit, and trigonometric substitutions. After this, there are multiple courses which follow, which include multivariable calculus, differential equations, real and complex analysis, linear and abstract algebra, , and geometry and topology.

No matter what path you choose, remember that calculus, and more generally mathematics is all around us, and keep on studying and remember to make your exams all Fiveable!

- Stewart, James.
*Calculus β Early Transcendentals, 8th Edition*. Cengage Publishing, 2016. - βAP Calculus AB and BC Course and Exam Description, Effective Fall 2019,β The College Board, 2019.Β

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π₯Unit 6 β Integration & Accumulation of Change

πUnit 7 β Differential Equations

πΆUnit 8 β Applications of Integration

π¦Unit 9 β Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)

βΎUnit 10 β Infinite Sequences & Series (BC Only)

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