hp40g+.book Page 26 Friday, December 9, 2005 1:03 AM
NOTE: The variable VX is now set to N. Reset it to X by | |
pressing | (to display CAS MODES screen) |
and change the INDEP VAR setting. | |
To check the result, we can say that: | |
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| ex – 1 | 1 | ||
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| lim | |||
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| x → 0 | x |
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| and that therefore: | ||||
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| 2 |
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| lim | en – 1 | = | 1 |
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| n → +∞ | 2 |
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| n |
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| or, simplifying: |
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| 2 | ⎞ |
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| lim | ⎛ | ⋅ n = 2 | |
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| ⎜en – 1⎟ | |||
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| n → +∞⎝ | ⎠ |
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| If the limit L of un exists as n approaches + ∞ in the | ||||
| inequalities in solution 2 above, we get: | ||||
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| 3 | 7 |
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| L ≤ | |||
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| 2 | 4 |
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Part 2 | 1. | Show that for every x in [0,2]: | |||
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| 2x + 3 |
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| = 2 – | |||
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| x + 2 |
| x + 2 | |
| 2. Find the value of: | ||||
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| 2 2x + 3 |
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| I = ∫0 x + 2 dx | |||
| 3. Show that for every x in [0,2]: | ||||
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| x | 2 |
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| 1 ≤ en ≤ en |
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| 4. | Deduce that: |
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| 1 ≤ un ≤ en ⋅ I |
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| 5. | Show that un is convergent and find its limit, L. | |||
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