then it is a vertical asymptote of the equation. If it does appear in the numerator, then it is a hole in the equation. In the example equation, solving x – 2 = 0 makes x = 2, which is a hole in the graph because the factor (x – ...
Infinite Discontinuity: An asymptote that the functions approaches infinitely but never reaches. This could be vertical or horizontal. Jump Discontinuity: There is a jump between two pieces of the curve resulting in a discontinuity. Case 2 Corners If a function has a sharp corner or cusp, the...
Your calculator will probably display “error” if you try it! This is how you know you’ve found an asymptote. We can also use this tangent identity to solve trigonometric identity puzzles, but we’ll get into those another time. Okay, before we go, let’s review some of the details:...
A limit does not exist if the function has a discontinuity, such as a hole or vertical asymptote, at the point where the limit is being evaluated. It can also not exist if the right-hand limit and left-hand limit approach different values, or if the function oscillates or becomes unbounde...