# hw5 - M421 HW 5 Due Friday Nov 9 From Wade Section Page...

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Unformatted text preview: M421 HW 5 Due Friday Nov. 9 From Wade Section Page Number Problems 11.1 329-330 4, 5 11.2 337-339 3, 4, 5, 6, 7 Non-book Exercises 1) For which α > 0 is the function f ( x,y ) = x 2 | y | α x 2 + | y | 3 ( x,y ) negationslash = 0 ( x,y ) = 0 , differentiable at zero? 2) Consider R ∞ = { vectorx = ( x 1 ,x 2 ,x 3 ,... ) vextendsingle vextendsingle vextendsingle x i ∈ R ,i = 1 , 2 , 3 ,... } . The l 2 norm on R ∞ is bardbl vectorx bardbl 2 = parenleftBigg ∞ summationdisplay i =1 | x i | 2 parenrightBigg 1 2 . The space l 2 = { vectorx ∈ R ∞ vextendsingle vextendsingle vextendsingle bardbl vectorx bardbl 2 < ∞} , is infinite dimensional. Show that the l 2 unit sphere, S = { vectorx ∈ l 2 vextendsingle vextendsingle vextendsingle bardbl vectorx bardbl 2 = 1 } , is closed, bounded, and not sequentially compact. That is, find a sequence from S which has no convergent subsequence....
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hw5 - M421 HW 5 Due Friday Nov 9 From Wade Section Page...

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