Vertical Asymptotes as Infinite Limits
If a function value approaches as approaches some value , then there is a vertical asymptote at . By testing values of on either side of , we can determine which direction the function is heading.
Enter a fucntion in the f(x) box. Drag the blue point on the x-axis to the location of the vertical asymptote. The two one-sided limits along with the overall limit are calculated and displayed. Now enter various test values of x to "approach" the vertical asymptote from one side or the other. Watch how the y-value changes as you get closer.