{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 256 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times " 1 14 0 0 0 1 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 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}{XPPEDIT 18 0 "f[n](x)" "-&%\"fG6#%\"nG6#%\"xG" }{TEXT -1 49 "\} of functions from a set S to R is said to " } {TEXT 259 18 "converge boundedly" }{TEXT -1 22 " to a function f if \+ \{" }{XPPEDIT 18 0 "f[n](x)" "-&%\"fG6#%\"nG6#%\"xG" }{TEXT -1 82 "\} \+ converges pointwise to f and it is possible to find a number K su ch that |" }{XPPEDIT 18 0 "f[n](x)" "-&%\"fG6#%\"nG6#%\"xG" }{TEXT -1 39 "| <= K for every x in S and every n.\011\n" }}{PARA 0 "" 0 "" {TEXT 260 19 "Uniform Convergence" }{TEXT -1 15 "\n\011\nA sequence \{ " }{XPPEDIT 18 0 "f[n](x)" "-&%\"fG6#%\"nG6#%\"xG" }{TEXT -1 48 "\} of functions from a set S to R is said to " }{TEXT 261 18 "converge \+ uniformly" }{TEXT -1 28 " to a function f if sup |" }{XPPEDIT 18 0 "f[n](x)" "-&%\"fG6#%\"nG6#%\"xG" }{TEXT -1 3 " - " }{TEXT 265 4 "f(x) " }{TEXT -1 42 " | tends to 0 as n tends to infinity.\011\n" }} {PARA 0 "" 0 "" {TEXT 262 10 "Exercise 1" }{TEXT -1 46 ": Demonstrate \+ that the sequence of functions " }{XPPEDIT 18 0 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