Three questions of advanced calculus
Prove using Definition 2.14 that lim n2 + 1 = +∞.
n→∞ n+1
2. (5 pts) Which three of the following statements, if combined,
imply that limn→∞ yn = −3? Prove your answer.
(A) x2n ≥ yn2 for every n
(B) yn − xn < n1 for every n
(C) limn→∞ xn = −3
(D) yn2 ≥ x2n for every n
3. (5 pts) Suppose that limn→∞ xn = 1. Prove using the definition
of limit (find N for every ε) that
lim 4xn −1 =−3.
n→∞ xn−2
SAMPLE ASSIGNMENT
