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8 | 8 | ## DBchapter(Infinite sequences and series) |
9 | 9 | ## DBsection(Integral test) |
10 | 10 | ## Date(6/3/2002) |
11 | | -## Institution(Univeristy of Utah) |
| 11 | +## Institution(University of Utah) |
12 | 12 | ## Author(Utah ww group) |
13 | 13 | ## Level(2) |
14 | 14 | ## TitleText1('Calculus') |
@@ -157,13 +157,15 @@ qa(~~@questions, ~~@answers, |
157 | 157 | ($ans1, $ans2, $ans3, $ans4, $ans5) = @answers[@slice] ; |
158 | 158 |
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159 | 159 | TEXT(EV3(<<'EOT')); |
160 | | -Test each of the following series for convergence by the Integral Test. |
161 | | -If the Integral Test can be applied to the series, enter CONV if |
| 160 | +Test each of the following series for convergence by the Integral Test. (Don't use any other tests.) |
| 161 | +If the Integral Test, by itself, can be applied to the series to determine whether it converges, enter CONV if |
162 | 162 | it converges or DIV if it diverges. |
163 | 163 | If the integral test cannot be applied to the series, enter NA. |
164 | | -(Note: this means that even if you know a given series converges |
165 | | -by some other test, but the Integral Test cannot be applied to it, |
166 | | -then you must enter NA rather than CONV.) $BR $BR |
| 164 | + |
| 165 | +$PAR(Note: this means that even if you know a given series converges |
| 166 | +by using some other test, or some other test combined with the integral test, |
| 167 | +but the integral test, all by itself, does not determine the answer |
| 168 | +then you must enter NA rather than CONV.) $PAR |
167 | 169 | EOT |
168 | 170 | TEXT(EV2(match_questions_list_varbox(10,@questions[@slice]))); |
169 | 171 |
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311 | 313 | if ($slice[$i] == 5) { |
312 | 314 | &SOLUTION(EV3(<<'EOT')); |
313 | 315 | ($j). The function \(f(x) = \frac{x+$f}{\left(-$g\right)^x}\) oscillates between |
314 | | -positive and negative values due to its denominator, so the Integral Test |
315 | | -does not apply. |
| 316 | +positive and negative values due to its denominator, so the integral test |
| 317 | +does not apply directly, so NA is the correct answer. |
| 318 | + |
| 319 | +$PAR (However the integral test can be used to show that the series converges $BBOLD absolutely |
| 320 | + $EBOLD, so the additional fact that $BQUOTE absolute convergence implies convergence $EQUOTE |
| 321 | +shows that the series does, in fact, converge.) |
316 | 322 |
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317 | 323 | EOT |
318 | 324 | } |
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