Approximating Error for Taylor Polynomials | Taylor's Inequality | Math with Professor V

In this video I go over Taylor's Inequality and how to approximate the error when using Taylor polynomials to represent functions. We'll work through several examples finding an upper bound on the error, determine how many terms we need in our approximation to guarantee error is less than a specified amount, and more! Need a recap of Taylor polynomials or Taylor series? I gotchu: Applications of Taylor Polynomials: https://youtu.be/FBTg0wue6lI?si=ziIjgQhqJOevA5Sm Taylor & Maclaurin Series: https://youtu.be/Wj6lerUoujc?si=_SgLkH8jhwAd-fsM Taylor & Maclaurin Series Part 1: https://youtu.be/8UEh0VejRMo?si=KJR-FjCCn-zC6PAT Taylor & Maclaurin Series/Binomial Series: https://youtu.be/37TLjCtCvW8?si=f7Fh2wh7mH29JK1z Don't forget to LIKE, Comment, & Subscribe! xoxo, Professor V https://linktr.ee/mathwithprofessorv Shop my Merch: https://math-with-professor-v.myspreadshop.com/ Playlist for Sequences & Series: https://youtube.com/playlist?list=PLl-Np5U6u5E5epcWgJmH-Ce-Gh-qFvUYx&si=ki8hPRoN2ycbVhz9 Calculus 2 Video Lectures: https://youtube.com/playlist?list=PLl-Np5U6u5E4z9zWlaf4Redf1iOwU720M&si=oA4XhGxW7_bARRbL Review of Sigma Notation: https://youtu.be/Iv6jSDSzoTs?si=C_1aUTgklyzOJUKd Full Video Lectures for Topics on Sequences & Series: Sequences: https://youtu.be/x39Pbv6dlj8?si=DMTjMY0IPXsWTM4e Monotonic and Bounded Sequences: https://youtu.be/3tfc5MY2sn0?si=cuWCPHMLo8sd3IWj The Ratio Test for Sequences: https://youtu.be/rsnDNv8WriA?si=P6eeK-zhIVA6ce9X Infinite Series: https://youtu.be/GFWWoDymGv0?si=wedIBgRvY9rcNSgs Telescoping Series: https://youtu.be/1ywKUgYFXa8?si=--AJhu4tG9BnB-L_ The Integral Test: https://youtu.be/Cr7g-USCovg?si=5y-li4UqdUSwT2I_ Comparison Tests: https://youtu.be/z6W6NX--7kg?si=938jyeeCquk2IzzX Comparison Tests Part 2: https://youtu.be/f_z7HcoDq0Y?si=ttwnFdFUF487GE3_ Alternating Series: https://youtu.be/H2FmTCXnA1g?si=FoQ4qaKlKAJHqUVQ Absolute Convergence/Ratio & Root Tests: https://youtu.be/1s3LR1NHzZQ?si=x_RU0M6L9tSHG_Kr Ratio Test Part 2: https://youtu.be/KnYFsOxKkPg?si=HE56GNcNl0S4CNI3 Root Test Part 2: https://youtu.be/jZ8vN9DOBzM?si=5dyNn49tdlkLFFhg Testing for Absolute & Conditional Convergence: https://youtu.be/bLASYus1jWw?si=3HnuSaKjfTSz2rc_ Strategy for Testing Series: https://youtu.be/zxDZAXRYvdw?si=IE3LHEMjCh2LBLUF More Strategy for Testing Series: https://youtu.be/peLhzHn0gB4?si=6WeSnIB6g4aOxWGT Power Series: https://youtu.be/xDM3s6h81Pg?si=mJASc7VADJbW2ive Finding the Radius & Interval of Convergence: https://youtu.be/DPjRGGOKY3c?si=OPlBCCxQC5vKZu2R Representation of Functions as Power Series: https://youtu.be/vvVmIbzRnzw?si=ILuH3Ut5LJ06s47g Differentiating and Integrating Power Series: https://youtu.be/_eGzguQ40_o?si=CQwRRtjiVLuy55RG Power Series MADE EASY!: https://youtu.be/vL-FYv-KKhA?si=OJib6jcw3fYOSJYs Taylor & Maclaurin Series Part 1: https://youtu.be/8UEh0VejRMo?si=KJR-FjCCn-zC6PAT Taylor & Maclaurin Series/Binomial Series: https://youtu.be/37TLjCtCvW8?si=f7Fh2wh7mH29JK1z More Taylor & Maclaurin Series: https://youtu.be/Wj6lerUoujc?si=_SgLkH8jhwAd-fsM Using Series to Evaluate Limits: https://youtu.be/edrKK20wqQI?si=ndv6kd4e19p7mmi9 Applications of Taylor Polynomials: https://youtu.be/FBTg0wue6lI?si=ziIjgQhqJOevA5Sm Calculus 1 Video Lectures: https://youtube.com/playlist?list=PLl-Np5U6u5E54PygbTaBsSzpSmVQVeJHq&si=1bevDEis2u9_Ul8V L'Hospital's Rule: https://youtu.be/S_0PgNru6LE?si=0zGL7F_9DvyQcL9l Infinite Limits: https://youtu.be/xd-Zo_MTP1E?si=omDXAPTIemTHE16A Limits at Infinity: https://youtu.be/IQKDJz3rOd0?si=LdY_1_mtP64u_oxA Calculus 3 Video Lectures: https://youtube.com/playlist?list=PLl-Np5U6u5E65pRRuD0mBXM4w4fenJ5gD #mathwithprofessorv #sequencesandseries #ratiotest #roottest #infiniteseries #integration #partialfractions #partialfractionmethod #partialfractiondecomposition #trigonometricsubstitution #trigintegrals #trigsubstitution #integrals #integralcalculus #calculus2 #calculusvideos #calculus2videos #integralvideos #trigonometricintegrals #math #youtubemath #mathvideos #mathprofessor #calculusvideos #integrationbyparts #integralcalculus #taylorsinequality Join this channel to get access to perks: https://www.youtube.com/channel/UCokuhoh5N_B0ZxHcEU_EWbQ/join Socials: IG: @mathwithprofessorv TikTok: @mathwithprofessorv I'm also an Amazon influencer, so feel free to support and shop: https://amazon.com/shop/mathwithprofessorv EXCITING NEWS: You can now sign up for my Patreon at the link below! https://www.patreon.com/mathwithprofessorv My Patreon is a place for students to have access to exclusive ad-free content not available on my YouTube channel! Access to the library of additional videos, worksheets, and more is available with the "Star Pupil Package" tier for just $9.99/month (USD). *This video is copy protected and cannot be downloaded or used in any capacity without my permission.*