Question : Use two repetitions of the Newton-Raphson algorithm to find the value of x near zero for which cosx = x : 2163553
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
21) Use two repetitions of the Newton-Raphson algorithm to find the value of x near zero for which cosx = x.
Enter just a real number rounded off to two decimal places.
22) Use two repetitions of the Newton-Raphson algorithm to find the value of x near zero for which ex = 2cosx.
Enter just a real number rounded off to two decimal places.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
23) Suppose that an investment of $1000 yields returns of $267.38, $343.28, and $500.00 at the end of the first, second, and third months, respectively. Determine the internal rate of return on this investment.
A) 5.9%
B) 4.59%
C) 5.13%
D) 4.9%
24) A mortgage of $123,981 is repaid in 300 monthly payments of $1000. Determine the monthly rate of interest.
A) 7.1%
B) 0.5%
C) 0.81%
D) 0.71%
Determine whether the given series converges or diverges, and find the sum if it converges.
25) 30 + 5 + (5/6) + (5/36) + ...
A) Converges; sum = 40
B) Converges; sum = 37
C) Converges; sum = 36
D) Converges; sum = 35.5
26) (1/23) + (4/23) + (16/23) + (64/23) + ...
A) Converges; sum = 2.78
B) Converges; sum = 3.98
C) Converges; sum = 3.70
D) Diverges
27) 1 + (1/7) + (1/49) + (1/343) + ...
A) Converges; sum = 1.75
B) Converges; sum = 1.3125
C) Converges; sum = 1.1667
D) Diverges
28) 13 + 7.8 + 4.68 + 2.808 + ...
A) Converges; sum = 32.5
B) Converges; sum = 19.5
C) Converges; sum = 48.75
D) Diverges
29) 0.98 + 0.0098 + 0.000098 + ...
A) Converges; sum = (49/50)
B) Converges; sum = (23/25)
C) Converges; sum = (98/99)
D) Diverges
Solve the problem.
30) The repeating decimal 0.44444... can be expressed as infinite geometric series
0.4 + 0.4((1/10)) + 0.4((1/10))2 + 0.4((1/10))3 + ... .
By finding the sum of the series, determine the rational number whose decimal expansion is 0.44444... .
A) (4/9)
B) (4/17)
C) (4/13)
D) (4/11)
31) The repeating decimal 0.90909090... can be expressed as infinite geometric series
0.90 + 0.90((1/100)) + 0.90((1/100))2 + 0.90((1/100))3 + ... .
By finding the sum of the series, determine the rational number whose decimal expansion is 0.90909090... .
A) (10/13)
B) (10/9)
C) (10/11)
D) (10/17)
32) Determine the sum of the series e-1 + e-2 + e-3 + ... if it converges.
A) diverges
B) (1/e - 1)
C) (e/e - 1)
D) e
33) Determine the sum of the series 
.
A) (e/e + 2)
B) 1 - (2/e)
C) (2/e)
D) none of these
34) Determine the sum of the series 
A) (2/3)
B) 3
C) - (3/2)
D) none of these
35) Determine the sum of the series 
A) (π/e - π)
B) (e/π)
C) (e/e - π)
D) none of these
36) Determine the sum of the series 1 + (1/1.01) + (1/(1.01)2) + (1/(1.01)3) + ... .
A) 10.1
B) 101
C) (1/1.01)
D) none of these
37) Determine the sum of the series 
A) 12
B) (3/4)
C) 3
D) (1/4)
38) Determine the sum of the series (1/2) + (1/22) + (1/23) + ... .
A) 1
B) 2
C) (1/2)
D) none of these
39) Determine the sum of the series 
A) (1/6)
B) (1/3)
C) (1/4)
D) none of these
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
40) Determine the sum of the following geometric series: 1 - (1/23) + (1/26) - (1/29) + (1/212) - ... .
Enter just a reduced fraction of form (a/b).
