Limits

Cal Journal Sept 25, 2011

In class we're working on limits, specifically the difference between limits coming from the left and right approaching a "cusp". A cusp is a sharp change in the graph where a tangeant line cannot be identified or makes drastic changes quickly. I found the graph below, and at x=2 theres a cusp in the graph. In problem 65 which we did for homework it states f(x)=.4x+k^2, if x<1 and kx+2.4, if x(>_) 1 and the problem ask you to find k. Since we know the limit is one, then k will be the same for both equations at 1. So if you plug in 1 for x you can use algebra to solve for k which comes out to be 2. This creates a graph with a cusp in it.