Lesson ten-Analysis of math-Volume I

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• published: 18 Oct 2013
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Limits strings Lemma Stolz - Cesaro, applying it in various forms. Raising indeterminacy of mathematics applicants various procedures                                          Application number 25 - Limit when n tends to infinity of variable (4 to the power of n plus 8n) / (3n 5n plus sixth power minus one); - No sense any shared infinity to infinity; - It gives the greatest common factor and the term exponential function tends to infinity faster than any exponential polynomial function if the base is greater than one; - Limit the initial sequence is infinite, the sequence is divergent;                                                 Method II -n variable is Replaced with the variable x Which Belongs to the set of real numbers and the computer Makes the graph function;                                                 Application number 26 - Limit the variable n tends to infinity of (1 +2 +3 +4 + ... + n) / (n cubed plus 2n plus one);   I do not sense any infinity divided by infinity; -Imply b (n) is unbounded, so the apply Stoltz-Cesaro's lemma; - Limit the initial string is zero, the sequence converges;                                                Application number 27 Variable limit when n tends to infinity of radical index n (n cubed plus two) / n;   I do not sense any zero infinite power; - Apply theorem (1) and then Stolz-Cesaro's lemma; - Limit is one initial sequence, the sequence is convergent;                                                   Method II -n variable is Replaced with the variable x Which Belongs to the set of real numbers and the computer Makes the graph function; -Function is Associated sequence chart, the graph is seen as a sequence boundary at infinity Asymptote horizontal branch.                                        Application number 28 - Mimic the variable n tends to infinity in (5n cubed plus 8n -1) / (n + 2 to the fourth power multiplied by n to the third power) tg (3.14n) / (n + fifth power -5 6n); - Limit the initial string is zero, the sequence converges;                                Method II                                          Method III -n variable is Replaced with the variable x Which Belongs to the set of real numbers and the computer Makes the graph function; -Function is Associated sequence chart, the graph is seen as a sequence boundary at infinity Asymptote horizontal branch.                                           Application number 29 Variable limit when n tends to infinity of (n +1 radical indicate three radical addition of n to the power of two minus one minus two) / (n +6); - No sense any shared infinity to infinity; -Abbreviated formula; Multiply top and bottom by-conjugate; - Limit is one initial sequence, the sequence is convergent;                                             Method II - It gives the greatest common factor term;                                                     Method III -n variable is Replaced with the variable x Which Belongs to the set of real numbers and the computer Makes the graph function; -Function is Associated sequence chart, the graph is seen as a sequence boundary at infinity Asymptote horizontal branch.