problem_set_4 - Name Section Student ID Last First MI Math...

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1 Name: First MI Last Student ID # Score Section: C REDIT 2 1 0 Problem #3 . Consider the two surfaces in space: S 1 : x 2 + y 2 = a 2 and S 2 : z = b 2 xy . These surfaces intersect on a curve in space, find a parametric representation for this curve. C REDIT 2 1 0 Problem #2 . Consider the two curves in R 3 which are parameterized as follows: C URVE 1: ( t ) = ( t , 1– t , 3+ t 2 ) C URVE 2: ( s ) = (3– s , s –2, s 2 ) with 0 ≤ s , t < ∞. Show that (by a miracle) these curves intersect – and find the point of intersection. C REDIT 2 1 0 Problem #1 . A particle spirals out from the origin according to x ( t ) = t cos t , y(t) = t sin t ; 0 ≤ t < ∞. Find expressions for the distance from the origin (which is not the arclength) and the speed as a function of t . Math 32A Lecture #5 Fall 2007 Problem Set #4
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2 Problem Set #4 C REDIT 2 1 0 Problem #4 . Consider the usual hyperbolic trig functions: cosh x 1 2 (e x e x ) sinh x 1 2 (e x e x ) . Derive the analog of the double angle formulas for these cases; that is to say expressions for cosh 2 x and sinh 2 x in terms of cosh x and sinh x .
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  • Fall '08
  • GANGliu
  • Math, Hyperbolic function

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