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Consider the function J: > R given through x Determine a function continuous continuation of f. Reason necessary! A9 (Function limits) Calculate the limit for the following functions f lim f(x). x + 1 In(x) a) /(x) b) /(x) x sin(x) A10 (Continuous functions) Let D = [0; and F defines D by F(x) = cost - exp(x) + 2. Show that F has exactly one root. A11 (pointwise and uniform convergence) Given is the function series (fa)nen defined by fn : (0,00) R. fa(x) === 1 n.r A12 Analyze the convergence behavior (pointwise or uniform) of the progression (fn) nEN on the sets a) 1) = (1.00), b) 1) = (0,00). Sketch f, forn=1,2,3.

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