defs1 - Sivakumar M151H Some definitions and theorems -...

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Unformatted text preview: Sivakumar M151H Some definitions and theorems - Exam 1 1. Let a = h a 1 ,a 2 i and b = h b 1 ,b 2 i . The dot product of a and b is defined as follows: a · b := a 1 b 1 + a 2 b 2 . 2. Let a and b be nonzero vectors, and let θ , 0 ≤ θ ≤ π , denote the angle between a and b . Then a · b = k a kk b k cos θ. 3. (i) Let a be a fixed real number, and suppose that a function f is defined in an interval containing a , except perhaps at a itself. We say that lim x → a f ( x ) = L ( L a real number) if, given > 0, there is a δ > 0 such that | f ( x )- L | < whenever 0 < | x- a | < δ . (ii) Let a be a fixed real number, and suppose that a function f is defined in an interval containing a , except perhaps at a itself. We say that lim x → a f ( x ) = + ∞ if, given M > 0, there is a δ > 0 such that f ( x ) > M whenever 0 < | x- a | < δ . (iii) Suppose that a function f is defined on the interval ( A, ∞ ) for some real number A . We say that lim x →∞ f ( x ) = L ( L a real number) if, given...
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This note was uploaded on 03/29/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.

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