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(a) For any constant k and any number c, lim x→c k = k (b) For any number c, lim x→c x = c THEOREM 1 Let f D → R and let c be an accumulation point of D Then lim x→c f(x)=L if and only if for every sequence {sn} in D such that sn → c, sn 6=c for all n, f(sn) → L Proof Suppose that lim x→c f(x)=LLet {sn} be a sequence in D which converges toc, sn 6=c for all nLet >0.

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U(x,y) = φ(x)h(y) is a solution of Laplace’s equation Substituting u(x,y) = φ(x)h(y) into the homogeneous boundary conditions, we get φ0(0)h(y) = 0, φ0(L)h(y) = 0, φ(x)h(0) = 0 It is no loss to assume that neither φnor his identically zero Then the boundary conditions are satisfied if and only if φ0(0) = φ0(L) = 0, h(0) = 0. Û à 4 s € ˛ ˚ d ^ ˙ ˙ ˛ ˚ ˜ " % – ” ™ fi " fl ì í î ï Ł g ı Œ Š ^ ⁄ ¥ & Ô j ' “ « ‹ › fi 3 & ø Ÿ Ž Ó Ô Õ Ò Ö ˙ ¨ ı 7 Ù › 3 † & fl V 3 ł ø › ˜ # š ¾ ƒ ˆ ’ ‚ ™ fi ˙ Ł Œ ˙ Ł Š ˙ Ł fi ˙ ı fi ˙ ★ł ™ œ š ž € ˙ ¨ ‚ 2 Ü ‰ 3 Ý â ¾ 4 s. US Space Force Selects ULA United Launch Alliance Wins MultiYear Competitive Contract Award to Launch Critical National Security Space Missions for the US Space Force Learn More Vulcan Centaur ULA is transforming the future of space launch, making it more affordable, accessible and commercialized with its new, nextgeneration rocket.

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