Taylor and Maclaurin Series

Definition of Taylor series: $$f(x) = f(a) + f'(a)(x-a) + \frac{f”(a)(x-a)^2}{2!} + \cdots +\frac{f^{(n-1)}(a)(x-a)^{n-1}}{(n-1)!} + R_n$$ $$R_n = \frac{f^{(n)}(\xi)(x-a)^n}{n!} \text{ where } a \leq \xi \leq x, \quad \text{ ( Lagrangue’s form )}$$ $$R_n = \frac{f^{(n)}(\xi)(x-\xi)^{n-1}(x-a)}{(n-1)!} \text{ where } a \leq \xi \leq x, \quad \text{ ( Cauch’s form )}$$ This result […]

How to Teach Calculus

When we talk about calculus, we must know that calculus deals with derivatives, infinite series, integrals and limits. All this, people learn in the first year of college. There is debate how calculus should be taught in high school because calculus have many advance over anything that has been taught before, but there is a […]

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