In an ideal world, I would like to have all students study limits in their pre-calculus course and know all about them when they get to calculus. Certainly, this would be better than teaching how to calculate derivatives in pre-calculus (after all derivatives are calculus, not pre-calculus). Limits are the foundation of the calculus. Continuity,…
A monster problem for Halloween. A while ago I suggested you look at , which using the dominance idea is zero. Of course your students may try graphing or a table. Here’s the graph done by a TI-Nspire CAS. Note the scales. This is not the way to go. Since the function is increasing near the…
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…
