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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 e^{x} = 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) + (1/2^{2}) + (1/2^{3}) + ... .

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 - (1/2^{3}) + (1/2^{6}) - (1/2^{9}) + (1/2^{12}) - ... .

Enter just a reduced fraction of form (a/b).