Infinitely Small Equivalents

This lecture introduces the concept of infinitely small equivalents, where two functions are considered equivalent if their limits approach zero in a given neighborhood. The instructor explains the definition and provides examples, such as the equivalence of sin(x) and x near x=0. The lecture also covers the comparison of geometric areas and the use of Infinitely Small Equivalents in limit calculations, showcasing examples like lim sin(2x) as 2x. Additionally, the lecture explores consequences like lim sin^2(2x) = 1-cos(3x) near x=0.