Unformatted text preview: sin θ ) = r 3 cos 2 θ sin θ r 4 cos 4 θ + r 2 sin 2 θ where things don’t cancel quite so nicely. We can try to pull out an r 2 factor, to get = r (cos 2 θ sin θ ) r 2 cos 4 θ + sin 2 θ . If sin θ stays bounded away from zero, then this goes to zero as r → (why?), but it is less clear what happens when r and sin θ 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
- Calculus, Sin, Continuous function