Calculus Solutions 26

Calculus Solutions 26 - Answers to Odd-Numbered Problems 23...

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Unformatted text preview: Answers to Odd-Numbered Problems 23 % = 0 w h e n t a n t = & ; f m , = 2 a t (i,$),fmin=-2at (-+,-'$) 1 25 (ax + by),, = W; (x2 + y2)min = 2 7 0 < c < f 29 The vectors head-to-tail form a 60-6@6O triangle. The outer angle is 120' 31 2 + &; 1 + fi; 1 + 35 Steiner point where the arcs meet 39 Best point for p = oo is equidistant from corners 4 1 grad f = (& ?+ y+ y,\/Z ?+ + 7); angles are 90-135-135 43 Third derivatives all 6; f = 5 x 3 + *x2 + $29 + 5 y3 1 2 3 3 45 (&)n(s)m ln(1- ~ y ) ] ~ , ~ = n!(n - I)! for rn = n > 0, other derivatives zero; f = -xy - 2 - 3 - . . 47 All derivatives are e2 at (1,l); f N e2[l + (x - 1) + (y - 1) + i ( x - 1)2 + (x - l)(y - 1) + ?(y - I ) ~ ] 4 9 x = l , y = - 1 : f,= 2, f, = -2, f,, = 2, fx, = 0, f, = 2; series must recover x2 + y2 51 Line x - 2y = constant; x + y = constant 5 3 ~ f . , + z y f x , + f f , , ] ~ , ~ ; f x , > O a n d f x z f u v > f ~ a t ( ~ , ~ ) ; f x = f v = O 5 5 A x = - l , A y = - 1 57 f = x2(12 - 42) has fmax = 16 at (2,4); line has slope -4, y...
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This document was uploaded on 11/02/2011 for the course MAC 2311 at University of Florida.

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