TheDerivative - Oxford University Press

Chapter4 RealAnalysis 281 51. Disprove the claim: If lim x→a |f(x)| = L, then either lim x→a f(x) = L or lim x→a f(x)= − L. 52. Iflim x→a f(x)= ∞ andlim x→a g(x)= ∞,thenlim x→a f +g = ∞. 53. Iflim x→a f(x)= ∞ andlim x→a g(x)= L ∈ R∗,thenlim x→a f(x) g(x) = ∞. 54. Iflim x→a f(x)= L,thenlim x→a (f(x)−L)= 0.55. Disprovethetwoclaims: (a) Iflim x→a f(x)= L ... ................
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