m25_q3_s

m25_q3_s - Math 2025 Quiz #3 (Fall 2004) Name: Inner...

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Unformatted text preview: Math 2025 Quiz #3 (Fall 2004) Name: Inner product on functions on [0,, b] (piecwise continuous, continous, etc.) is given by (f, g) : fab fltlgfi) dt. The norm is "m b Hm=¢mnz fmet If A is a subset. of R” then the indicator function of A is the function XA : R“ -> R” given by 1 ifteA “(75) z {o ifteé/l In the following we will always use a = 0 and b : 1. A) Evaluate the following inner products: a ‘ W ‘ W(W“L%flflflh= i Lim-zilmfl (2) Let f(t) = t2 and g(z€) : t + 1. Then (fig) 2 ; 7 (3) Let flt) = X[0,1/2) {75) and 9“) = X{o,i/4)(tl “ X[1/4,1/2)(t)- What is (fig) 2 Q B) Determine which of the following pair of vectors are orthogonal. (nurtaca—m “W (2) fit) : sin('27rt) and g(t) : cos(27rt); Vfig‘ (3) m) z t2 — 1 and 905) :t; No C) Evaluate the following norms: mun—m=”€2 ; (2) li(27374)1%= ; Egg J, cwmw= ggefig <9 {ixcfl‘} “3 SK’X N, U1) Hwa {MSWM‘ €31 £3 Layavi) Lmléi i a “I "I .~ 3 i t 55% w «5&3? 3“” m“ m “m : ¥C E WW 0 K1 m '2: 49x“ (*9; a? w) 31%” :U‘ dim m (:2 gm '3 ‘7‘ ‘T’ i W is: r: P) am J“ » "° we 5 “i 3 ¥$Qwfifiwflhwfi“#ézzw m1.qu C _ “a 2.. ) A} Mafia)“ 3, Q) (m0 ._. 2 ...
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m25_q3_s - Math 2025 Quiz #3 (Fall 2004) Name: Inner...

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