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1:00
Easy Taylor Series Approximation Example: Learn How to Approximate Functions
904 views
Jul 16, 2023
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mathswithmuza on Instagram: "The Taylor series is a way to approximate a function as an infinite sum of polynomial terms based on its derivatives at a single point. It is commonly expanded around x = 0, which is called the Maclaurin series. Given a function f(x), its Taylor series expansion around x = a is written as: f(x) = f(a) + f’(a)(x - a) + f’’(a)/2! * (x - a)^2 + f’’’(a)/3! * (x - a)^3 + … Each term involves a derivative of the function evaluated at x = a, divided by the corresponding fac
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mathswithmuza on Instagram: "A Taylor series is a way to approximate a function by expressing it as an infinite sum of polynomial terms based on the function’s derivatives at a single point. Starting from that point, usually called the center, the first term is the function’s value there, the next term involves its first derivative, and so on, with higher derivatives capturing more detail about the function’s behavior. This method allows complex functions, like exponentials, trigonometric functi
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Mathematisa | Math Animations on Instagram: "✨ Taylor Series for sin(x) ✨ The Taylor series provides a way to express a function as an infinite sum of terms built from its derivatives at a specific point. ✍️ When this expansion is taken around zero, it’s called the Maclaurin series. 🔹 This technique lets us approximate functions using polynomials, where each term involves higher-order derivatives divided by factorials. For sin(x): 👉 The Maclaurin expansion contains only odd powers, with altern
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