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Question : Find the area under the graph of y = xe^-x^2 for x : 2163459

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

45) Consider . Which of the following is true?

A) The limit diverges.

B) The limit exists and is equal to zero.

C) none of these

D) The limit exists and is equal to two.

E) The limit exists and is equal to one.

Evaluate the improper integral whenever it is convergent. If it is divergent, state this.

A) 0

B) -11

C) 11

D) Divergent

47) dx Give your answer in exact form.

A) -e^{-10}

B) (e^{-10}/5)

C) 0

D) Divergent

A) 2e^{-3/2}

B) e^{-1}

C) divergent

D) e^{-3/2}

E) none of these

49)

A) divergent

B) -1

C) 0

D) 1

50)

A) (1/2)

B) 0

C) (1/4)

D) divergent

E) 1

51)

A) (2/ln2)

B) 2ln2

C) divergent

D) (ln2/2)

E) ln2

52)

A) 2ln2

B) divergent

C) (1/2)(ln2)^{2}

D) (1/ln2)

53) dx

A) 0

B) divergent

C) 1

D) -1

E) (1/10)

54) dx

A) 2

B) divergent

C) 1

D) 0

E) -1

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

55)

Enter your answer as just a reduced fraction or the word "divergent".

56) dx

Enter your answer as just a reduced fraction or the word "divergent".

57)

Enter your answer as just a reduced fraction or the word "divergent".

58) dx

Enter your answer as an integer or the word "divergent".

59) dx

Enter your answer as a reduced fraction or the word "divergent".

60)

Enter your answer as a reduced fraction or the word "divergent".

61) dx

Enter your answer as a reduced fraction or the word "divergent".

62)

Enter your answer as a reduced quotient or the word "divergent".

63)

Enter your answer as a reduced fraction or the word "divergent".

64) Recall that the capital value of an asset is given by If the annual rate of earnings, K(t), of a certain machine is $3000 and if the interest rate is 12%, find the capital interest of the machine.

Enter just an integer representing dollars (no units).

65) Find the area under the graph of y = 4e^{-3x} for x ≥ 1. Enter your answer as ae^{b} with any fractions reduced of form (a/b).

66) Find the area under the graph of y = xe^{-x^2} for x ≥ 0. Enter just a reduced fraction.