Or When is a limit not a limit? I was discussing the definition of a limit equal to infinity with someone recently. It occurred to me that such functions have no limit! Of course, you say that’s why – sometimes – we say “infinity”. But should we? What does “∞” mean? The definition we were…
Students get confused about infinity, , because they think of it as a number, because used like a number. Even though they know there is no largest number, they think of infinity as the largest number. In studying limits, the starting point of calculus, infinite limits come up early on. We tell them . But…
When considering functions made up of the sums, differences, products or quotients of different sorts of functions (polynomials, exponentials and logarithms), or different powers of the same sort of function we say that one function dominates the other. This means that as x approaches infinity or negative infinity, the graph will eventually look like the dominating function. Exponentials…
Ways to find limits (summary): If the function is continuous at the value x approaches, then substitute that value and the number you get will be the limit. If the function is not continuous at the value x approaches, then If you get something that is not zero divided by zero, the limit does not exist (DNE) or…
Teaching Calculus 