» Esercizi svolti di Matematica e Fisica

Computation of a limit by comparison of infinities

Gennaio 20th, 2021 | by Marcello Colozzo |

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Exercise

Calculate the following limits of fig. 1.

Solution
The first limit gives rise to the indeterminate form oo/oo) (infinity over infinity). Indeed:

We manipulate the analytic expression of the assigned function:

for which

For x ->+oo the logarithm is an infinity of infinitely small order (with respect to the reference infinity u(x)=x)

Conclusion:

The calculation of the other limit is immediate:

Tags: Computation of a limit by comparison of infinities

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