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Chapter 7: Q 86 (page 593)

Use the result of Example 7to approximate the levels of the drug Excellent麓e during the first week, assuming the dosages and decay rates in Exercises localid="1654346363996" 86-88.

localid="1654346369210" L1=200,p=50.

Short Answer

Expert verified

For L1=200,p=50, approximate level's of drug during the first week are as following :-

L1=200,L2=300,L3=350,L4=375,L5=388,L6=394andL7=397.

Step by step solution

01

Step 1. Given Information

We have given that :-

L1=200,p=50

By using the result of example 7we have to approximate the drug Excellent'e during the first week.

02

Step 2. Approximate level's of drug during the first week.

We have L1=200,p=50.

In example 7, we find the following result :-

L1=DandLk+1=1-p100Lk+Dfork鈮�1

By using this result we have the following :-

L2=1-50100200+200鈬�L2=300

L3=1-50100300+200鈬�L3=350

L4=1-50100350+200鈬�L4=375

L5=1-50100375+200鈬�L5=387.5鈮�388

L6=1-50100388+200鈬�L6=394

and

L7=1-50100394+200鈬�L7=397

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Most popular questions from this chapter

For a convergent series satisfying the conditions of the integral test, why is every remainder Rnpositive? How can Rnbe used along with the term Sn from the sequence of partial sums to understand the quality of the approximation Sn?

Find an example of a continuous function f :[1,鈭�)鈫�Rsuch that 鈭�1鈭�fxdxdiverges and localid="1649077247585" 鈭�k=1鈭�fkconverges.

True/False:

Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: If ak鈫�0, then 鈭�k=1鈭�akconverges.

(b) True or False: If 鈭�k=1鈭�akconverges, then ak鈫�0.

(c) True or False: The improper integral 鈭�1鈭�f(x)dxconverges if and only if the series 鈭�k=1鈭�f(k)converges.

(d) True or False: The harmonic series converges.

(e) True or False: If p>1, the series 鈭�k=1鈭�k-pconverges.

(f) True or False: If f(x)鈫�0as x鈫�鈭�, then 鈭�k=1鈭�f(k) converges.

(g) True or False: If 鈭�k=1鈭�f(k)converges, then f(x)鈫�0as x鈫�鈭�.

(h) True or False: If 鈭�k=1鈭�ak=Land {Sn}is the sequence of partial sums for the series, then the sequence of remainders {L-Sn}converges to 0.

For each series in Exercises 44鈥�47, do each of the following:

(a) Use the integral test to show that the series converges.

(b) Use the 10th term in the sequence of partial sums to approximate the sum of the series.

(c) Use Theorem 7.31 to find a bound on the tenth remainder,R10.

(d) Use your answers from parts (b) and (c) to find an interval containing the sum of the series.

(e) Find the smallest value of n so thatRn鈮�10-6

鈭�k=1鈭�1k2

Find the values of x for which the series鈭�k=0鈭�xkconverges.
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