A trigonometric limit is a mathematical concept that describes the behavior of a trigonometric function as the independent variable approaches a certain value. It helps determine the value that the function approaches as the input value gets closer and closer to the specified value.
Trigonometric limits are evaluated using algebraic and trigonometric identities, as well as common limit rules such as the sum, difference, and product rules. In some cases, trigonometric limits can also be evaluated using L'Hospital's rule.
A left-sided trigonometric limit is when the independent variable approaches a certain value from the left side, while a right-sided trigonometric limit is when the independent variable approaches the value from the right side. In other words, the direction of approach determines whether it is a left-sided or right-sided limit.
A trigonometric limit at infinity is when the independent variable approaches positive or negative infinity, and the function is evaluated at that value. This type of limit helps determine the long-term behavior of a trigonometric function as the input value becomes extremely large or small.
Trigonometric limits are important in calculus because they help determine the continuity and differentiability of a function at a certain point, which are crucial concepts in calculus. They also help evaluate important mathematical properties such as the slope of a curve and the area under a curve.