Unformatted text preview: 3.5.7 . We apply Lemma 3.5.8 to the vectors −→ v = ∂ −→ p ∂s −→ w = ∂ −→ p ∂t to ±nd a positive, continuous function K ( s,t ) de±ned on the domain of −→ p such that for every θ the vector −→ v ( s,t,θ ) = (cos θ ) ∂ −→ p ∂s ( s,t ) + (sin θ ) ∂ −→ p ∂t ( s,t ) has b −→ v ( s,t,θ ) b ≥ K ( s,t ) . In particular, given s , t , and an angle θ , we know that some component of the vector −→ v ( s,t,θ ) must have absolute value exceeding K ( s,t ) / 2:  v j ( s,t,θ )  > K ( s,t ) 2 ....
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 Fall '08
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 Calculus, Derivative, Cos, Continuous function, vw

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