Find limits using addition, subtraction, and multiplication laws

Learning Objectives State the Sum, Difference, and Product Laws for limits. Apply the Sum Law to find the limit of a sum of functions. Apply the Difference Law to find the limit of a difference of functions. Apply the Product Law to find the limit of a product of functions. Combine the Sum, Difference, and Product Laws to evaluate limits of polynomial functions. Deconstruct complex limit problems into simpler parts using the limit laws. Verify that individual limits exist as finite numbers before applying the laws. Ever wondered how complex systems are analyzed by breaking them down into simpler parts? 🤔 That's exactly what we're doing with limits today! This tutorial will introduce you to the fundamental laws of limits: the Sum, Difference, and Product Laws. Y...

TermDefinitionExample LimitThe value that a function `f(x)` approaches as the input `x` approaches some value `c`.The limit of `f(x) = x^2` as `x` approaches 2 is 4, written as `lim_{x->2} x^2 = 4`. Limit LawsA set of rules for evaluating limits of combined functions (sums, differences, products, etc.) by breaking them into simpler limits.The Sum Law allows us to find the limit of `f(x) + g(x)` by adding their individual limits. Existence of a LimitThe condition that for a limit law to apply, the individual limits must exist as finite, real numbers.If `lim_{x->c} f(x) = L` and `lim_{x->c} g(x) = M`, where L and M are real numbers, then their individual limits exist. Polynomial FunctionA function involving only the operations of addition, subtraction, multiplication, and non-negat...

Sum Law for Limits lim_{x->c} [f(x) + g(x)] = lim_{x->c} f(x) + lim_{x->c} g(x) The limit of a sum is the sum of the limits, provided the individual limits of f(x) and g(x) exist. Difference Law for Limits lim_{x->c} [f(x) - g(x)] = lim_{x->c} f(x) - lim_{x->c} g(x) The limit of a difference is the difference of the limits, provided the individual limits of f(x) and g(x) exist. Product Law for Limits lim_{x->c} [f(x) * g(x)] = [lim_{x->c} f(x)] * [lim_{x->c} g(x)] The limit of a product is the product of the limits, provided the individual limits of f(x) and g(x) exist.