solution (by vo Ren 62. Dilutg operation: Ren them with 2 L 41, an=e-n cos n a.
ID: 2860043 • Letter: S
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solution (by vo Ren 62. Dilutg operation: Ren them with 2 L 41, an=e-n cos n a. Let Cn be th nth replacer of the seque 2n + 2 45-52. Geometric sequences Determine whether the follo sequences converge or diverge, and state whether the or whether they oscillat, Give thel e whether they are monotoric it when the sequence converge b. After how n 15%? reach 15%? c. Determine t solution that ge? rge? or whether they oscillate. Give the limit when the sequence com ts45. (0.2") 1.2) 47. (0.7 63-68. Growth rates of the following seque /{5(-1.01)"} 49..(1.00001") 150 (2+13 51. (-2.5)" state that they diverge. 53. 100(-0.003)" 63. 53-58. Squeeze Theorem Find the limit of the following sequences /n /2 cos n 54. in 6 es or 69-74. Formal proofs of a sequence to prove 69, lim-=0 cos (nT/2 2 tan n n sin(2 Vn 159. Periodic dosing Many people take aspirin on a regular preventive measure for heart disease. Suppose a persol 80 mg of aspirin every 24 hours. Assume also that aspini half-life of 24 hours; that is, every 24 hours, half of the the blood is eliminated. S on a regular basis as half of the drug in a. Find a recurrence relation for the sequence (da) tha the amount of drug in the blood after the nth dose d, b. Using a calculator, determine the limit of the sequene 80. Further Explorations 5. Explain why or wh e true andg a. If lim an 1 ar I. If lim a" 0 an c. The convergent se first 100 terms, bu long run, how much drug is in the person's blo c. Confirm the result of part (b) by finding the d limit of (d, directly A car loan Marie takes out a $20,000 loan for a a new car. The uivalently, a edhe current mhal. B60. loan has an annual interest rate of 6% or, equiva,interest interest rate of 0.5%. Each month, the bank a loan balance (the interest is always 0.5% of the the loan and then Marie makes a $200 payment to ance. Let B, be the loan balance immediately a ment, where B= $20,000. te of 6% or, equivalently, a of the current balan 20d payment to reduce the loan diately after the nth pay a. Write the first five terms of the sequence e b. Find a recu d. If {an} = ve terms of the sequence {BB a recurrence relation that generates Determine hm Determine ence relation that generates the secque the at generates the sequeeExplanation / Answer
10.) Divide numerator and denominator by n^12
So, we will get
1/(3 + 4/n^12)
As n tends to infinity
We will get limit = 1/3
12.) We can write it as
e^-n + 2
So, as n tends to infinity e^(-n) tends to 0
So, we get limit as 2
14.) k/sqrt(9k^2+1)
Divide it by k for both numerator and denominator,
1/sqrt ( 9 + 1/k^2)
As k tends to infinity,
We will get 1/ sqrt 9
= 1/3
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