Question - Limit Calculation at Infinity
Solution:
\[
\lim_{{x \to \infty}} \frac{{2x + 1}}{{4x + 5}} = \frac{{\frac{{2x}}{{x}} + \frac{{1}}{{x}}}}{{\frac{{4x}}{{x}} + \frac{{5}}{{x}}}}
\]
\[
= \frac{{2 + \frac{{1}}{{x}}}}{{4 + \frac{{5}}{{x}}}}
\]
\[
= \frac{{2}}{{4}} \quad \text{quand } x \to \infty
\]
\[
= \frac{1}{2}
\]
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