Limits and Derivatives

Derivatives represent the rate of change

Derivatives represent the rate of change of a function. Using the example of a falling body with distance s = 4.9t², we find velocity by calculating a

The limit of a function f(x)

The limit of a function f(x) as x approaches 'a' is the value that f(x) gets arbitrarily close to. Written as lim(x→a) f(x) = L. Both left-hand and ri

Limits follow algebraic rules

Limits follow algebraic rules: limit of sum equals sum of limits, limit of product equals product of limits, and limit of quotient equals quotient of

Key limit formulas include

Key limit formulas include: lim(x→a) (xⁿ - aⁿ)/(x - a) = naⁿ⁻¹, lim(x→0) sin x/x = 1, and lim(x→0) (1 - cos x)/x = 0.

The derivative of f(x) at point

The derivative of f(x) at point 'a' is f'(a) = lim(h→0) [f(a+h) - f(a)]/h, provided this limit exists. This is called the first principle of derivativ