π Finding the Third-Degree Taylor Polynomial for f(x) = e^(4x) π
In this video, I walk through the process of finding the third-degree Taylor polynomial for the function f(x) = e^(4x), centered at x = 0. This example shows how to apply the Taylor series formula to compute a polynomial approximation of an exponential function.
π Whatβs covered:
Step-by-step derivation of the Taylor series for e^(4x).
Detailed explanation of how to compute the third-degree Taylor polynomial.
How to find higher-order derivatives and use them to build the polynomial approximation.
Understanding Taylor polynomials is essential in calculus for approximating functions, so this is a great exercise to strengthen your skills in series expansions and polynomial approximations.
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