Prove by definition (epsilon-delta) the next limits:

1. lim(x-->inf) {(2x^2-11x-11)/(4x^2+11x-1)} = 1/2

2. lim(x-->1) {(x^3-3x)/(x^2-2x+1)} = -inf

Thanks!

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- January 9th 2010, 01:42 PMAlso sprach ZarathustraLimits by definition.
Prove by definition (epsilon-delta) the next limits:

1. lim(x-->inf) {(2x^2-11x-11)/(4x^2+11x-1)} = 1/2

2. lim(x-->1) {(x^3-3x)/(x^2-2x+1)} = -inf

Thanks! - January 9th 2010, 01:57 PMDrexel28
For the first one note that, . Now, . So, let be given. Choosing ensures that . We may conclude that . Using similar techniques we may conclude that . We may therefore conclude that

For the second one, note that which for a sufficiently small neighborhood around is strictly less than . So, let be given, then choosing ensures that . The conclusion follows.

P.S. Technically, the second should be - January 9th 2010, 02:06 PMAlso sprach Zarathustra
\left|2-\frac{11}{x^2}-\frac{11}{x}-2\right|=\left|\frac{11}{x^2}+\frac{11}{x}\right|\ leqslant\frac{22}{x} Wy is that? |2-....-2| ???

- January 9th 2010, 02:07 PMDrexel28
- January 9th 2010, 02:22 PMAlso sprach Zarathustra
Sorry!

- January 9th 2010, 02:23 PMDrexel28