Power series ultimate study guide

Power series representations of functions, and their radius and interval of convergence. These examples include the power series of tan^-1(x), power Series of ln(1+x), power Series of 1/(1-x), power Series of cos(x), power series of sin(x), power series of e^(x), binomial series, power series of sinh(x), power series of cosh(x), and more! You definitely should know all these power series examples for your Calculus 2 class. Best wishes to you! The File: 👉 https://www.patreon.com/posts/file-to-26-2-95154336? 1/(1-x) Power series for you t-shirt 👉 https://a.co/d/ga2kCjq intro: 0:00 Q1, Power Series of x/(1-4x) at a=0, 0:47 Q2, Power Series of x^4/(9+x^2) at a=0, 6:00 Q3, Power Series of (1+2x)/(1-x) at a=0, 10:58 Q4, Power Series of 1/(x^2-5x-6) at a=0, 17:45 Q5, Power Series of 1/(1-x)^2 by partial fractions at a=0, 27:17 Q6, Power Series of ln(1+x) at a=0, 33:17 Q7, Power Series of tan^-1(x) at a=0, 45:56 Q8, Power Series of 1/(1-x) at a=3, 56:02 Q9, Power Series of 1/x^2 at a=-2, 1:04:10 Q10, Power Series of 1/(x^2+6x+10) at a=-3, 1:22:26 Q11, Power Series of e^x at a=0, 1:25:20 Q12, Power Series of sin(x) at a=0, 1:32:50 Q13, Power Series of cos(x) at a=0, 1:43:10 Q14, Power Series of e^(3x) at a=2, 1:46:35 Q15, Power Series of sin(x) at a=pi/2, 1:52:42 Q16, Power Series of sin(x) at a=-pi, 1:59:02 Q17, Power Series of sin^2(x) at a=0, 2:04:07 Q18, Power Series of cos(x) at a=pi/4, 2:09:54 Q19, Power Series of sinh(x) at a=0, 2:20:43 Q20, Power Series of cosh(x) at a=0, 2:27:58 Q21, Power Series of tanh^-1(x) at a=0, 2:31:46 Q22, Power Series of ln(x) at a=2, 2:41:50 Q23, Power Series of 2x^3-5x^2+1 at a=1, 2:48:45 Q24, Power Series of (1+x)^r, i.e. the binomial series, at a=0, 2:56:33 Q25, Power Series of sqrt(4+x) at a=0, 3:12:29 Q26, Power Series of sin^-1(x) at a=0, 3:17:34 Q26.2, Power Series of x^0.2 at a=26, 3:31:50 End Tejava black tea & 2019 Long Beach Marathon Medal 3:34:50 --------------------------------------------------------------------------------------------------- ***Thanks to ALL my lovely patrons for supporting my channel and believing in what I do*** AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff Julian Moik Hiu Fung Lam Ronald Bryant Jan Řehák Robert Toltowicz Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi Skorj Olafsen --------------------------------------------------------------------------------------------------- 💪 If you would also like to support this channel and have your name in the video description, then you could become my patron here https://www.patreon.com/blackpenredpen