Question

How do you find vertical asymptotes using limits?

Answer 1

To find vertical asymptotes using limits, determine the values of x for which the function approaches positive or negative infinity. The vertical asymptote occurs at these values of x.

Step-by-step explanation:

To find vertical asymptotes using limits, you need to determine the values of x for which the function approaches positive or negative infinity. The vertical asymptote occurs at these values of x. Here is a step-by-step process:

1. Determine the limits of the function as x approaches positive and negative infinity.
2. If the limit is positive or negative infinity, find the x-values at which the function approaches these limits.
3. These x-values are the vertical asymptotes of the function.

For example, let's consider the function y = 1/x. As x approaches zero, y approaches positive infinity. As x approaches positive or negative infinity, y approaches zero. Therefore, the vertical asymptote of the function is x = 0.