Barrons AP Calculus

(Marvins-Underground-K-12) #1

for the right-hand limit of f at c (as x approaches c through values greater than

Example 1 __

The greatest-integer function g(x) = [x], shown in Figure N2–1, has different
left-hand and right-hand limits at every integer. For example,

This function, therefore, does not have a limit at x = 1 or, by the same reasoning,
at any other integer.

Figure  N2–1

However, [x] does have a limit at every nonintegral real number. For example,

Example 2 __

Suppose the function y = f (x), graphed in Figure N2–2, is defined as follows:

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