ch01 - Contents 1 Limits 1.1 Motivation Tangent and velocity 1.2 Limit of a function with intuitive denition 1.3 The precise denition of a limit 1.4

ch01 - Contents 1 Limits 1.1 Motivation Tangent and...

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Contents 1. Limits 1 1.1. Motivation: Tangent and velocity 1 1.2. Limit of a function with intuitive definition 2 1.3. The precise definition of a limit 4 1.4. Calculating limits with limit laws 5 1.5. Continuity 7 1.LimitsThe entire calculus is built on the concept of limit. In this chapter, we will discussWhat 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
2 Next, 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.

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