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Unformatted text preview: sin ) = r 3 cos 2 sin r 4 cos 4 + r 2 sin 2 where things dont cancel quite so nicely. We can try to pull out an r 2 factor, to get = r (cos 2 sin ) r 2 cos 4 + sin 2 . If sin stays bounded away from zero, then this goes to zero as r (why?), but it is less clear what happens when r and sin both tend to zero. Recall that a function is continuous at a point x in its domain if lim x x f ( x ) = f ( x ) ....
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- Fall '08