A limit is a fundamental concept in calculus that describes the behavior of a function as the input approaches a specific value. It tells us the value that a function is approaching, rather than the actual value at that point.
To find the limit of a function, you can use algebraic manipulation, graphing, or mathematical rules such as L'Hôpital's rule. You can also use a table of values to estimate the limit. However, the most accurate way to find a limit is using the formal definition, which involves evaluating the function at values that are closer and closer to the desired input value.
A derivative is a mathematical concept that represents the instantaneous rate of change of a function at a specific point. It is the slope of the tangent line to the graph of the function at that point.
To find the derivative of a function, you can use the power rule, product rule, quotient rule, or chain rule. You can also use the definition of a derivative, which involves taking the limit of the difference quotient as the change in input approaches zero.
Limits and derivatives are closely related in calculus. The derivative of a function at a specific point is the limit of the difference quotient as the change in input approaches zero. In other words, the derivative is a special type of limit. The concept of a limit is essential for understanding and calculating derivatives.