Calculus is a tool that helps us understand how a change in one quantity is related to a change in another. How does the speed of a falling object change as a function of time? How does the level of water in a barrel change as a function of the amount of liquid poured into it? we see change occurring in nearly everything we observe in the universe.
we also see that the need of limits arise when we finding the instantaneous rate of change of a function or the tangent to a curve.
definitions of limits:
- the function approaches the limit L near a, if we can make f(x) as close as we like to L by requiring that x be sufficiently close, but not equal to a
is f(x) continues at x limits
