The Taylor Series Formula
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From the Calculus II: Taylor & Maclaurin Series curriculum
<h2>Approximating Functions</h2>
<p>A Taylor series allows us to represent complex functions (like sin(x) or e^x) as an infinite sum of polynomial terms. This is how calculators compute Sine and Cosine!</p>
<h3>General Formula (centered at a):</h3>
<p>f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...</p>
<h3>Maclaurin Series (centered at 0):</h3>
<p>A special case where a = 0. Example for e^x:</p>
<pre>e^x ≈ 1 + x + x^2/2! + x^3/3! + ...</pre>
Frequently asked about The Taylor Series Formula
Approximating Functions A Taylor series allows us to represent complex functions (like sin(x) or e^x) as an infinite sum of polynomial terms. This is how calculators compute Sine and Cosine! General Formula (centered at a): f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! Read the full notes above for the details.
The Taylor Series Formula is a core topic in Calculus II: Taylor & Maclaurin Series. Most exam papers test it via a mix of definitions, worked examples, and applied problems. The notes above cover the high-yield sub-topics, common pitfalls, and the kind of questions examiners typically set.
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