Question

How to find horizontal asymptotes of sin(1/x) graphs?

Answer 1

To find the horizontal asymptotes of the sin(1/x) graph, analyze the behavior of the function as x approaches positive and negative infinity. The graph does not have any horizontal asymptotes.

Step-by-step explanation:

The horizontal asymptotes of the graph of the function y = sin(1/x) can be found by examining the behavior of the function as x approaches positive and negative infinity.

1. As x approaches positive infinity, 1/x approaches 0. Since the sine function has a maximum value of 1 and a minimum value of -1, the graph of sin(1/x) oscillates between -1 and 1 infinitely as x approaches infinity. Therefore, there is no horizontal asymptote in this case.
2. As x approaches negative infinity, 1/x approaches 0. Again, the graph of sin(1/x) oscillates between -1 and 1 infinitely. So, there is no horizontal asymptote in this case either.

In conclusion, the graph of sin(1/x) does not have any horizontal asymptotes.