Taylor SeriesMatching a function with the polynomial whose derivatives agree at a point.MathematicsNear a, a smooth function is approximated by thepolynomial whose derivatives at a match its own.f(x) = Σ f⁽ⁿ⁾(a)(x − a)ⁿ / n!e^x about 01 + x + x²/2 + x³/6 + …Valid for every x.sin x about 0x − x³/6 + x⁵/120 − …Odd powers only.1/(1 − x) about 01 + x + x² + x³ + …Only for |x| < 1.THE COMMON MISTAKE✗ Assuming a smooth function equals its series✓ Checking that the remainder tends to zeroThe function e^(−1/x²), extended by f(0) = 0, is smooth with every derivativezero at 0, so its Taylor series is 0 and matches nowhere else.Maclaurin is the case a = 0. The radius of convergence is fixed by thenearest singularity, in the complex plane if not the real line.Taylor Serieslearnposters.com
Taylor Series — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the Taylor Series poster

The rule, 3 worked examples, and the mistake everyone makes.

Maclaurin is the case a = 0. The radius of convergence is fixed by the nearest singularity, in the complex plane if not the real line.

Questions about the Taylor Series poster

What’s on the Taylor Series poster?
The rule, 3 worked examples, and the mistake everyone makes. Near a, a smooth function is approximated by the polynomial whose derivatives at a ma…; f(x) = Σ f⁽ⁿ⁾(a)(x − a)ⁿ / n!; e^x about 0 = 1 + x + x²/2 + x³/6 + …; sin x about 0 = x − x³/6 + x⁵/120 − …; 1/(1 − x) about 0 = 1 + x + x² + x³ + …; Common mistake: Assuming a smooth function equals its series → Checking that the rema…. Maclaurin is the case a = 0. The radius of convergence is fixed by the nearest singularity, in the complex plane if not the real line.
Who is the Taylor Series poster for?
Taylor Series belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning calculus can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Taylor Series poster?
For approximations, limits, and any expansion around a specific centre. A wall chart earns its place by being glanceable from where the work is happening, so Taylor Series belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Taylor Series?
The Chain Rule, Derivative Rules and Fundamental Theorem sit alongside Taylor Series in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.The Chain RuleDerivative RulesFundamental Theorem
Is the Taylor Series poster free to download and print?
Yes. Taylor Series downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Taylor Series poster print at?
Taylor Series is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Taylor Series loses nothing.Printing guide

Related posters

Charts that sit alongside Taylor Series on the same wall.

Browse every Mathematics poster, or start from the full catalogue.