Function Approximation: Order 5

This lecture presents an example of calculating the fifth-order Taylor expansion of a given function around zero. The instructor demonstrates the step-by-step process of finding the expansion, starting from the function definition and applying the necessary mathematical operations. The lecture emphasizes the importance of understanding the properties of the function, such as being odd or even, to determine the coefficients in the expansion. Various trigonometric functions are used in the example, showcasing the application of Taylor series in approximating complex functions. The lecture concludes with the final expression of the Taylor expansion and highlights the significance of each term in the series.