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- Prove using the ϵ−n0 definition that the sequence Xn=(9−7n)/(8−13n) converges, and find its limit.. Let gn = nχ[1/n,2/n] and g = 0. Show thatZ 20g 6= limn→∞ Z 20gn.Does the sequence (gn) converge uniformly to g? Does the Monotone Convergence Theoremapply? Does Fatou’s Lemma apply?Under what condition does eat converge to 0 as t->infinity? a = 0 a > 0 a < 0 a <= 0