Limits

A limit is the value that a function approaches as its input approaches a specific point. Limits are fundamental in calculus because they allow us to define the derivative and integral. The concept of a limit helps in understanding instantaneous rates of change and areas under curves.

The equation of a tangent to a curve at any point is given by: First, find the derivative of the given function : At , the slope of the tangent is: Now, substitute into the tangent equation: Thus, the equation of the tangent line is: This corresponds to the equation .