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{SECT 0 {PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 
11 "Math 2270-2" }}{PARA 258 "" 0 "" {TEXT -1 25 "Solution Template, p
art B" }}{PARA 259 "" 0 "" {TEXT -1 20 "Inner Product Spaces" }}{PARA 
0 "" 0 "" {TEXT 256 23 "Type in your name here:" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
257 93 "1)  Using the \"dot1\" inner product, find an orthonormal basi
s for P3 = span\{1, t, t^2, t^3\}. " }{TEXT -1 1 " " }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 258 47 "2)  Find the projection of f(t)=sin(t) onto P3." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT 259 138 "3)  Compare the distance between sin(t) and i
ts projection onto P3, to the distance between sin(t) and its degree t
hree Taylor polynomial." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 260 67 "4)  Display the thr
ee functions from (3) together in a single plot." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 0 "" {TEXT -1 
231 "5)  Using the \"dot2\" inner product, MAPLE, and pencil and paper
 if necessary, find the projection which is the degree 10 Fourier poly
nomial for the absolute value function  f(t)=|t|.  Hint: which of thes
e coefficients must be zero?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 261 87 "6)  Create a d
isplay which shows the graph of f and of its Fourier polynomial, from \+
#5." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 261 "" 0 "" {TEXT -1 213 "7)  Have MAPLE compute the derivative
 of your Fourier polynomial, and then plot this derivative function.  \+
Does this graph seem to be related to the graph of the derivative of t
he absolute value function? Explain." }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
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2 33 1 1 }