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Unformatted text preview: (a) Use the binomial expansion (or another technique you are familiar with) to simplify 11 √ 1x , where x ± 1. ( 10 points ) (b) The Taylor series approximation is deﬁned as : f ( x ) ≈ f ( a )+( xa ) ∂f ∂x  x = a + ··· . What is the second order Taylor expansion of cos θ at θ = 0 ? ( 10 points ) (c) For small values of x ( x ± 1) what is a a good approximation for sin( x ) ( 10 points ) 2 Physics 3101, HW#1, Fri, Jan 8 2009 Name: Problem 3: Mathematical Background II (30 points) (a)→ V 1 = ( v 1 x ,v 1 y ,v 1 z ) ,→ V 2 = ( v 2 x ,v 2 y ,v 2 z ). What is ± ± ±→ V 1 ± ± ± ?, what is→ V 1 ·→ V 2 ?, what is→ V 1→ V 2 ? ( 10 points ) (b) Find N ( t ), given dN dt ∝ N ( t ) ( 10 points ) (c) Find the general solution to m d 2 x dt 2 =kx ( 10 points ) 3...
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This note was uploaded on 03/30/2010 for the course PHY 3101 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff
 Physics, Work

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