Limits in calculus refer to the value that a function approaches as the input of the function gets closer and closer to a specific value. They are used to determine the behavior of a function near a certain point.
The most common types of limits are one-sided limits, where the input approaches the specific value from only one side, and two-sided limits, where the input approaches the specific value from both sides.
To find the limit of a function, you can either use algebraic methods such as factoring and canceling out common terms, or you can use graphical methods by plotting the function and observing its behavior near the specific value.
Indeterminate forms in limits occur when the limit of a function cannot be determined by direct substitution. These include forms such as 0/0, ∞/∞, and ∞ - ∞. They require additional algebraic manipulations or the use of L'Hopital's rule to solve.
Limits are important in mathematics because they allow us to understand the behavior of functions and make precise calculations even when the function is not defined at a certain point. They are also crucial in many real-life applications, such as in economics and physics.