Continuity and Differentiability.

13 lessons104 min2 simulations

A function is continuous at a point when its graph arrives there without a break: the left-hand limit, the right-hand limit and the value all agree. It is differentiable there when the slopes of the chords on both sides settle on one finite number. This chapter tests continuity, shows that sums, products, quotients and composites of continuous functions stay continuous, proves that differentiable implies continuous, and builds the full toolkit of differentiation: the chain rule, implicit functions, inverse trigonometric functions, eˣ and log x, logarithmic differentiation, parametric forms and second derivatives.

Also called: continuity · differentiability · chain rule