hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM
Exercise 8 | For this exercise, make sure that the calculator is in exact | ||||||||||
| real mode with X as the current variable. | ||||||||||
Part 1 | For an integer, n, define the following: | ||||||||||
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| x |
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| 2 | 2x + 3 |
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| un | = ∫ |
| n | dx | ||||||
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| 0 | x + 2 |
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| Define g over [0,2] where: | ||||||||||
| g(x) = |
| 2x + 3 |
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| x + 2 |
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| 1. Find the variations of g over [0,2]. Show that for | ||||||||||
| every real x in [0,2]: | ||||||||||
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| 2. Show that for every real x in [0,2]: | ||||||||||
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| n | ≤ g(x)e | n |
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3. After integration, show that:
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3 | ⎛ |
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| n | ≤ u |
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⎜ne |
| – n⎟ | n | ≤ | ⎜ne |
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2 | ⎝ |
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4. Using: |
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lim | ex | – 1 | = 1 |
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x → 0 |
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show that if un has a limit L as n approaches infinity, then:
≤ ≤ 7 3 L
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