Deck 6: Extension F: Applications of Integration

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سؤال
A manufacturer of light bulbs wants to produce bulbs that last about <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> hours but,of course,some bulbs burn out faster than others.Let <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> be the fraction of the company's bulbs that burn out before t hours. <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> lies between 0 and 1. Let <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> What is the value of <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> ?

A) <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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سؤال
Determine whether the improper integral converges or diverges,and if it converges,find its value. <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B)   C) Diverges D)   <div style=padding-top: 35px>

A) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B)   C) Diverges D)   <div style=padding-top: 35px>
B) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B)   C) Diverges D)   <div style=padding-top: 35px>
C) Diverges
D) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B)   C) Diverges D)   <div style=padding-top: 35px>
سؤال
Determine whether the improper integral converges or diverges,and if it converges,find its value. <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A) 0 B) Diverges C)   D)   <div style=padding-top: 35px>

A) 0
B) Diverges
C) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A) 0 B) Diverges C)   D)   <div style=padding-top: 35px>
D) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A) 0 B) Diverges C)   D)   <div style=padding-top: 35px>
سؤال
Determine whether the improper integral converges or diverges,and if it converges,find its value. <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A) 0 B) Diverges C) 6 D) 3 <div style=padding-top: 35px>

A) 0
B) Diverges
C) 6
D) 3
سؤال
Let a and b be real numbers.What integral must appear in place of the question mark "?" to make the following statement true? <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these <div style=padding-top: 35px>

A) <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these <div style=padding-top: 35px>
B) <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these <div style=padding-top: 35px>
C) <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these <div style=padding-top: 35px>
D) <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these <div style=padding-top: 35px>
E) none of these
سؤال
Evaluate the integral or show that it is divergent. Evaluate the integral or show that it is divergent.   <div style=padding-top: 35px>
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Deck 6: Extension F: Applications of Integration
1
A manufacturer of light bulbs wants to produce bulbs that last about <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)   hours but,of course,some bulbs burn out faster than others.Let <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)   be the fraction of the company's bulbs that burn out before t hours. <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)   lies between 0 and 1. Let <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)   What is the value of <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)   ?

A) <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)
B) <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)
C) <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)
D) <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)
E) <strong>A manufacturer of light bulbs wants to produce bulbs that last about   hours but,of course,some bulbs burn out faster than others.Let   be the fraction of the company's bulbs that burn out before t hours.   lies between 0 and 1. Let   What is the value of   ?</strong> A)   B)   C)   D)   E)
2
Determine whether the improper integral converges or diverges,and if it converges,find its value. <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B)   C) Diverges D)

A) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B)   C) Diverges D)
B) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B)   C) Diverges D)
C) Diverges
D) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B)   C) Diverges D)
3
Determine whether the improper integral converges or diverges,and if it converges,find its value. <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A) 0 B) Diverges C)   D)

A) 0
B) Diverges
C) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A) 0 B) Diverges C)   D)
D) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A) 0 B) Diverges C)   D)
4
Determine whether the improper integral converges or diverges,and if it converges,find its value. <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A) 0 B) Diverges C) 6 D) 3

A) 0
B) Diverges
C) 6
D) 3
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5
Let a and b be real numbers.What integral must appear in place of the question mark "?" to make the following statement true? <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these

A) <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these
B) <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these
C) <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these
D) <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these
E) none of these
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6
Evaluate the integral or show that it is divergent. Evaluate the integral or show that it is divergent.
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