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X i. ð í ì ì s/ ï x ì ï ò ô x î í ò ò ô x õ ï ì í ð x ó î õ ð ñ í x ô ó. MATH 140B HW 5 SOLUTIONS Problem1(WR Ch 7 #8) If I(x) ˘ 0 (x •0),1 (x ¨0),if {xn} is a sequence of distinct points of (a,b), and ifP jcnj converges, prove that the series f (x) ˘ X1 n˘1 cnI(x¡xn) (a •x •b) converges uniformly, and that f is continuous for every x 6˘xn Solution Let fk(x) ˘ Xk n˘1 cnI(x¡xn) By the Weierstrass Mtest (Theorem 710) with Mn ˘jcnj, {fk(x. R u o W P Z u } µ Á u X } u & Æ W ð ô ì r î ï ó r ô ô õ ï W,K E/y U W Z } v W ð ô ì r î ï ó r ô ô ô ô dZ E^dz> dZ E^WKZd d/KE d^zZ W dZ E^dz> U /E X^ · W Kd · W í ó í ñ ì õ ï t W Á Á Á X v Ç o X } u.

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