We will see soon what happens when h becomes smaller and smaller and that the continuity will not deteriorate. Indeed, we will see that we get closer and closer to the cos function.

Continuity Def: A function f (x) is continuous at x = a if the following three condi-tions all hold:

One more theorem is worth noting: the one that says sums, products, scalar multiples and compositions of continuous functions are continuous. For knowing this gives us a way to check …

Continuity of algebraic operations: Constant functions are continuous. The one-variable function taking x to 1/x is continuous except at x = 0. The addition function R2 → R taking (x, y) to x + y …

Feb 28, 2024 · n 2.18. Continuity Note. In this section, we define the continuity of a function similar to the way . t is done in Calculus 1. Remember that we have a slightly different …

Continuity and Combinations of Functions Theorem If f and g are continuous at a and c is a constant, then the following functions are also continuous at a:

So there’s some additional property we need in order to make sure we can evaluate limits in this way. This property is called continuity. If you’ve seen continuity before, it might be clear to you …