Contents1.Limits11.1.Motivation: Tangent and velocity11.2.Limit of a function with intuitive definition21.3.The precise definition of a limit41.4.Calculating limits with limit laws51.5.Continuity71.LimitsThe entire calculus is built on the concept of limit. In this chapter, we will discuss•What is limit?•How to calculate limit?Q: In general, one can not say that a tangent is a line that touch the curve once andonly once. Why?Example 1.1.Find an equation of the tangent line to the parabolay=x2at the pointP(1,1).1
2Next, we see how to find velocity from given distance function.Example 1.2.Suppose a car is moving on a straight line from starting fromOto theright. The distance of the car fromOafter timetseconds is given bys(t) = 4.9t2meter.Find theinstantaneous velocityof the car att= 5second.