Limits and Derivatives

Calculus begins: limits built from left- and right-hand approach, the algebra of limits, factor-cancellation, the workhorse $\lim_{x \to a}\frac{x^n - a^n}{x - a} = na^{n-1}$ and the fundamental $\lim_{x \to 0}\frac{\sin x}{x} = 1$, then the derivative as a limit — first principles, the rules of differentiation, and the standard table through the trig family. The foundation of all Class 12 calculus.