Thomas 2 - Limits & Continuity

"The concept of a limit is a central idea that distinguishes calculus from algebra & trig. It is fundamental to finding the tangent to a curve or the velocity of an object. We develop the limit, first intuitively, and then formally. We use limits to describe the way a function f varies. Some functions vary continuously; small changes in "x" produce only small changes in f(x). Other functions can have values that jump or vary erratically. The notion of a limit gives a precise definition to distinguish between these behaviors. The geometric application of using limits to define the tangent to a curve leads at once to the important concept of the derivative of a function. The derivative quantifies the way a function's values change."
(George Thomas)

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