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Use the Ratio Test to determine the convergence or divergence of the series. ​ Use the Ratio Test to determine the convergence or divergence of the series. ​ ​ A) ​Diverges. B) Converges. C) ​Ratio Test is inconclusive. ​


A) ​Diverges.
B) Converges.
C) ​Ratio Test is inconclusive.

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​Test the series ​Test the series for convergence or divergence using any appropriate test. ​ A) ​diverges B) ​converges for convergence or divergence using any appropriate test. ​


A) ​diverges
B) ​converges

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​Find the radius of convergence centered at ​Find the radius of convergence centered at for the following function. ​ ​ A) ​4 B) ​2 C) ​0 D) ​1 E) ​ for the following function. ​ ​Find the radius of convergence centered at for the following function. ​ ​ A) ​4 B) ​2 C) ​0 D) ​1 E) ​ ​


A) ​4
B) ​2
C) ​0
D) ​1
E) ​ ​Find the radius of convergence centered at for the following function. ​ ​ A) ​4 B) ​2 C) ​0 D) ​1 E) ​

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What are the next three terms in the arithmetic sequence -2,-6,-10,.... ​​


A) ​-14, -18, -22
B) ​2, 6, 10
C) ​56, -224, 896
D) ​-8, -10, -12
E) -10,-14,-18

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A

​Find the radius of convergence of the series ​Find the radius of convergence of the series ​ A) ​1 B) ​2 C) ​3 D) ​7 E) ​9 ​


A) ​1
B) ​2
C) ​3
D) ​7
E) ​9

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​Find the radius of convergence centered at ​Find the radius of convergence centered at for the following function. ​ ​ A) ​4 B) ​2 C) ​0 D) ​1 E) ​ for the following function. ​ ​Find the radius of convergence centered at for the following function. ​ ​ A) ​4 B) ​2 C) ​0 D) ​1 E) ​ ​


A) ​4
B) ​2
C) ​0
D) ​1
E) ​ ​Find the radius of convergence centered at for the following function. ​ ​ A) ​4 B) ​2 C) ​0 D) ​1 E) ​

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Find the limit of the following sequence. ​ Find the limit of the following sequence. ​ ​ A) B) C) D) E) The limit does not exist. ​


A) Find the limit of the following sequence. ​ ​ A) B) C) D) E) The limit does not exist.
B) Find the limit of the following sequence. ​ ​ A) B) C) D) E) The limit does not exist.
C) Find the limit of the following sequence. ​ ​ A) B) C) D) E) The limit does not exist.
D) Find the limit of the following sequence. ​ ​ A) B) C) D) E) The limit does not exist.
E) The limit does not exist.

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Use the Ratio Test to determine the convergence or divergence of the series. ​ Use the Ratio Test to determine the convergence or divergence of the series. ​ ​ A) ​The series converges. B) The series diverges. ​


A) ​The series converges.
B) The series diverges.

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​​Determine the convergence or divergence of the following series. ​ ​​Determine the convergence or divergence of the following series. ​ ​ A) ​inconclusive B) ​converges C) ​diverges ​


A) ​inconclusive
B) ​converges
C) ​diverges

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Write an expression for the ​nth term of the sequence Write an expression for the ​nth term of the sequence , , , ,.... ​​ A) ​ B) ​ C) ​ D) ​ E) , Write an expression for the ​nth term of the sequence , , , ,.... ​​ A) ​ B) ​ C) ​ D) ​ E) , Write an expression for the ​nth term of the sequence , , , ,.... ​​ A) ​ B) ​ C) ​ D) ​ E) , Write an expression for the ​nth term of the sequence , , , ,.... ​​ A) ​ B) ​ C) ​ D) ​ E) ,.... ​​


A) ​ Write an expression for the ​nth term of the sequence , , , ,.... ​​ A) ​ B) ​ C) ​ D) ​ E)
B) ​ Write an expression for the ​nth term of the sequence , , , ,.... ​​ A) ​ B) ​ C) ​ D) ​ E)
C) ​ Write an expression for the ​nth term of the sequence , , , ,.... ​​ A) ​ B) ​ C) ​ D) ​ E)
D) ​ Write an expression for the ​nth term of the sequence , , , ,.... ​​ A) ​ B) ​ C) ​ D) ​ E)
E) Write an expression for the ​nth term of the sequence , , , ,.... ​​ A) ​ B) ​ C) ​ D) ​ E)

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​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , , ​


A) ​ ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , , , ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , , , ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , , , ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , ,
B) ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , , , ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , , , ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , , , ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , ,
C) ​​ ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , , , ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , , , ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , , , ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , ,
D) ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , , , ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , , , ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , , , ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , ,
E) ​​ ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , , , ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , , , ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , , , ​Find the Taylor polynomials (centred at zero) of degree (a) 1,(b) 2,(c) 3,and (d) 4. ​ ​ A) ​ , , , B) , , , C) ​​ , , , D) , , , E) ​​ , , ,

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Complete two iterations of Newton´s Method for the function Complete two iterations of Newton´s Method for the function using the initial guess 2.9. ​ ​ A) ​3.001834, 2.9998 B) ​3.001864, 3.0002 C) ​3.001864, 3.0001 D) ​3.001724, 3 E) ​3.001514,2.9999 using the initial guess 2.9. ​ ​


A) ​3.001834, 2.9998
B) ​3.001864, 3.0002
C) ​3.001864, 3.0001
D) ​3.001724, 3
E) ​3.001514,2.9999

Correct Answer

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Write an expression for the ​nth term of the sequence 4,24,124,624,.... ​​


A) ​ Write an expression for the ​nth term of the sequence 4,24,124,624,.... ​​ A) ​ B) ​ C) ​ D) ​ E)
B) ​ Write an expression for the ​nth term of the sequence 4,24,124,624,.... ​​ A) ​ B) ​ C) ​ D) ​ E)
C) ​ Write an expression for the ​nth term of the sequence 4,24,124,624,.... ​​ A) ​ B) ​ C) ​ D) ​ E)
D) ​ Write an expression for the ​nth term of the sequence 4,24,124,624,.... ​​ A) ​ B) ​ C) ​ D) ​ E)
E) Write an expression for the ​nth term of the sequence 4,24,124,624,.... ​​ A) ​ B) ​ C) ​ D) ​ E)

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The annual spending by tourists in a resort city is 900 million dollars.Approximately 75% of that revenue is again spent in the resort city,and of that amount approximately 75% is again spent in the resort city.If this pattern continues,write the geometric series that gives the total amount of spending generated by the 900 million dollars (including the initial outlay of 900 million dollars) and find the sum of the series.


A) The geometric series is The annual spending by tourists in a resort city is 900 million dollars.Approximately 75% of that revenue is again spent in the resort city,and of that amount approximately 75% is again spent in the resort city.If this pattern continues,write the geometric series that gives the total amount of spending generated by the 900 million dollars (including the initial outlay of 900 million dollars) and find the sum of the series. A) The geometric series is The sum of the series is $3600 million. B) The geometric series is The sum of the series is $67,500 million. C) The geometric series is The sum of the series is 3600 million. D) The geometric series is The sum of the series is $67,500 million. E) The geometric series is The sum of the series is $675 million. The sum of the series is $3600 million.
B) The geometric series is The annual spending by tourists in a resort city is 900 million dollars.Approximately 75% of that revenue is again spent in the resort city,and of that amount approximately 75% is again spent in the resort city.If this pattern continues,write the geometric series that gives the total amount of spending generated by the 900 million dollars (including the initial outlay of 900 million dollars) and find the sum of the series. A) The geometric series is The sum of the series is $3600 million. B) The geometric series is The sum of the series is $67,500 million. C) The geometric series is The sum of the series is 3600 million. D) The geometric series is The sum of the series is $67,500 million. E) The geometric series is The sum of the series is $675 million. The sum of the series is $67,500 million.
C) The geometric series is The annual spending by tourists in a resort city is 900 million dollars.Approximately 75% of that revenue is again spent in the resort city,and of that amount approximately 75% is again spent in the resort city.If this pattern continues,write the geometric series that gives the total amount of spending generated by the 900 million dollars (including the initial outlay of 900 million dollars) and find the sum of the series. A) The geometric series is The sum of the series is $3600 million. B) The geometric series is The sum of the series is $67,500 million. C) The geometric series is The sum of the series is 3600 million. D) The geometric series is The sum of the series is $67,500 million. E) The geometric series is The sum of the series is $675 million. The sum of the series is 3600 million.
D) The geometric series is The annual spending by tourists in a resort city is 900 million dollars.Approximately 75% of that revenue is again spent in the resort city,and of that amount approximately 75% is again spent in the resort city.If this pattern continues,write the geometric series that gives the total amount of spending generated by the 900 million dollars (including the initial outlay of 900 million dollars) and find the sum of the series. A) The geometric series is The sum of the series is $3600 million. B) The geometric series is The sum of the series is $67,500 million. C) The geometric series is The sum of the series is 3600 million. D) The geometric series is The sum of the series is $67,500 million. E) The geometric series is The sum of the series is $675 million. The sum of the series is $67,500 million.
E) The geometric series is The annual spending by tourists in a resort city is 900 million dollars.Approximately 75% of that revenue is again spent in the resort city,and of that amount approximately 75% is again spent in the resort city.If this pattern continues,write the geometric series that gives the total amount of spending generated by the 900 million dollars (including the initial outlay of 900 million dollars) and find the sum of the series. A) The geometric series is The sum of the series is $3600 million. B) The geometric series is The sum of the series is $67,500 million. C) The geometric series is The sum of the series is 3600 million. D) The geometric series is The sum of the series is $67,500 million. E) The geometric series is The sum of the series is $675 million. The sum of the series is $675 million.

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​Use the sixth-degree Taylor polynomial centered at ​Use the sixth-degree Taylor polynomial centered at for the function to approximate Round your answer to nearest ten thousandth. ​ A) ​0.2295 B) ​0.2197 C) ​0.2397 D) ​0.1185 E) ​0.1436 for the function ​Use the sixth-degree Taylor polynomial centered at for the function to approximate Round your answer to nearest ten thousandth. ​ A) ​0.2295 B) ​0.2197 C) ​0.2397 D) ​0.1185 E) ​0.1436 to approximate ​Use the sixth-degree Taylor polynomial centered at for the function to approximate Round your answer to nearest ten thousandth. ​ A) ​0.2295 B) ​0.2197 C) ​0.2397 D) ​0.1185 E) ​0.1436 Round your answer to nearest ten thousandth. ​


A) ​0.2295
B) ​0.2197
C) ​0.2397
D) ​0.1185
E) ​0.1436

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The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails. ​ The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails. ​ ​ ​ A) B) C) D) E) ​ The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails. ​ ​ ​ A) B) C) D) E) ​


A) The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails. ​ ​ ​ A) B) C) D) E)
B) The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails. ​ ​ ​ A) B) C) D) E)
C) The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails. ​ ​ ​ A) B) C) D) E)
D) The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails. ​ ​ ​ A) B) C) D) E)
E) The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails. ​ ​ ​ A) B) C) D) E)

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​Find the power series for the function ​Find the power series for the function using the power series for ​ A) ​ B) ​ C) ​ D) ​ E) ​ using the power series for ​Find the power series for the function using the power series for ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​


A) ​ ​Find the power series for the function using the power series for ​ A) ​ B) ​ C) ​ D) ​ E) ​
B) ​ ​Find the power series for the function using the power series for ​ A) ​ B) ​ C) ​ D) ​ E) ​
C) ​ ​Find the power series for the function using the power series for ​ A) ​ B) ​ C) ​ D) ​ E) ​
D) ​ ​Find the power series for the function using the power series for ​ A) ​ B) ​ C) ​ D) ​ E) ​
E) ​ ​Find the power series for the function using the power series for ​ A) ​ B) ​ C) ​ D) ​ E) ​

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​Determine the convergence or divergence of the series ​Determine the convergence or divergence of the series Use a symbolic algebra utility to verify your result. ​​ A) ​The series diverges. B) ​The series converges. Use a symbolic algebra utility to verify your result. ​​


A) ​The series diverges.
B) ​The series converges.

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Find the next three terms of the geometric sequence 8,40,200,.... ​​


A) ​232, 264, 296
B) ​1,000, 5,000, 25,000
C) ​360, 520, 680
D) ​205, 210, 215
E) 200,1,000,5,000

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B

Find the radius of convergence of the series ​ Find the radius of convergence of the series ​ ​ A) ​16 B) ​18 C) ​1 D) ​9 E) ​8 ​


A) ​16
B) ​18
C) ​1
D) ​9
E) ​8

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E

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