The limit of a trigonometric function represents the value the function approaches as the input approaches a specific value. We can define the limit of a...
The limit of a trigonometric function represents the value the function approaches as the input approaches a specific value. We can define the limit of a trigonometric function in two ways:
One-sided limits: The limit of a trigonometric function is equal to the value the function approaches as the input approaches the positive or negative infinity, but not both.
Two-sided limits: The limit of a trigonometric function is equal to the value the function approaches as the input approaches the positive or negative infinity.
For example, consider the trigonometric function
One-sided limits:
As
As
Two-sided limits:
The limit of the trigonometric function as it approaches infinity is equal to the limit as it approaches negative infinity, which is equal to 0. This is because the function oscillates between 1 and -1 as it approaches infinity.
These one-sided and two-sided limits provide important information about the behavior of trigonometric functions. For example, the limit of the trigonometric function as it approaches infinity tells us that the function approaches 0 as the input approaches infinity