#5 from the Internet can contain viruses. Unless you need to edit, it's safer to stay in Protected View.Enable EditingMath 4303 Homework Section 4.2 Limit Theorems1. Use the limit theorems (or homework from 4.1) to show that lim2n – 4n² –5converges. Hint: Do notnm - 3n' +7n +1use the definition.2. Use the limit theorems (or homework from 4.1) to show that lim5n2+4nconverges. Hint: Do not use then00 7n3+6definition.2an3. Use the limit theorems (or homework from 4.1) to show that limn100 32n Converges. Hint: Do not use thedefinition.4. Use the limit theorems (or homework from 4.1) to show that lim (Vn2 + n – n) converges. Hint: Do notn00use the definition.5. Prove Theorem 4.2.1 (a) Suppose that s,} and {t,} are sequences of real numbers, with lim s, =s andlim t, =t, then lim (s, +t,) = s +t6. Prove Theorem 4.2.1 (c) Suppose that s,} and {t,} are sequences of real numbers, with lim s, = s andlim t, =t, then lim (s, t,) = st7. Prove Theorem 4.2.1 (c) Suppose that s, and t, are sequences of real numbers, with lim s, =s andlim t, =t, limカー→の t。provided t, # 0, t#0 Vn8. Prove: Theorem 4.2.7 (The Ratio Test) Suppose {x,is a sequence of positive terms wherelim= L <1 Then lim x, =01→のOFocus

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Description: #5 from the Internet can contain viruses. Unless you need to edit, it's safer to stay in Protected View.Enable EditingMath 4303 Homework Section 4.2 Limit Theorems1. Use the limit theorems (or homework from 4.1) to show that lim2n – 4n² –5converges.