To prove that sine is continuous, we need to show that limxla sin x sin a
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To prove that sine is continuous, we need to show that limxla sin x − sin a for every real number a. By Exercise 63 an equivalent statement is that
Use (6) to show that this is true.
Exercise 63
Prove that f is continuous at a if and only if
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lim sin(a + h) = sin a lim f(a + h) = f (a)
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