Q12. Let f: R R such that f(x + y) = f (x) + f...

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Q12. Let f: R → R such that f(x + y) = f (x) + f (y), Vx, y E R and let lim f be exists. (1) Show that lim f = 0 %3D (2) Show that lim f = f(c), Vc ER (Hint: For Part (1): Show that f(nx) = nf (x),Vn E N and then replace x by 1 and then use the Sequential Criterion) n Q12. Let f: R → R such that f(x + y) = f (x) + f (y), Vx, y E R and let lim f be exists. (1) Show that lim f = 0 %3D (2) Show that lim f = f(c), Vc ER (Hint: For Part (1): Show that f(nx) = nf (x),Vn E N and then replace x by 1 and then use the Sequential Criterion) n