Multiple choice questions Ali Akbar Alijani Department of Mathematics, University of Guilan e-mail: alijanialiakbar@gmail.com Hossein Sahleh Department of Mathematics, University of Guilan e-mail: sahleh@guilan.ac.ir Question 1. Let f,g : R → R be two periodic functions with periods a and b, respectively, such that lim x→0 f (x) x = u and lim x→0 g(x) x = v 6= 0. What is the value of lim n→∞ f ((3+ √ 7) n a) g((2+ √ 2) n b) ? 1. 0 2. 3+ √ 7 2+ √ 2 3. 1 4. The above sequence is divergent. Question 2. What is the value of ∑ ∞ 1 n n 4 +n 2 +1 ? 1. 1 2 2. 1 4 3. 1 8 4. The above series is divergent. Question 3. Let (X, d) be a metric space,A ⊆ X and > 0 arbitrary. Which of the following statements is true about O  (A)= {x ∈ X ; d(x, a) <} and C  (A)= {x ∈ X ; d(x, a) ≤ }? 1