Example Question - infinity
Here are examples of questions we've helped users solve.
Finding the Limit as x Approaches Infinity
\[ \begin{align*} 2 \cdot \lim_{{x \to +\infty}} \left( \frac{1}{2x} \right) &= 2 \cdot \lim_{{x \to +\infty}} \left( \frac{1}{2} \cdot \frac{1}{x} \right) \\ &= 2 \cdot \left( \frac{1}{2} \cdot \lim_{{x \to +\infty}} \frac{1}{x} \right) \\ &= 2 \cdot \left( \frac{1}{2} \cdot 0 \right) \\ &= 2 \cdot 0 \\ &= 0 \end{align*} \]
Analysis of a Limit as x Approaches Infinity
<p>\[ \lim_{{x \to +\infty}} \frac{2}{x} = \frac{2}{+\infty} \]</p> <p>\[ = 0 \]</p>
Evaluating the Limit of a Function as x Approaches Infinity
<p>La question demande d'évaluer la limite suivante :</p> <p>\[2 \lim_{x \to \infty} \left( \frac{1}{2x} \right)\]</p> <p>Pour résoudre cette limite, on suit les étapes suivantes :</p> <p>\[2 \lim_{x \to \infty} \left( \frac{1}{2x} \right) = 2 \cdot \lim_{x \to \infty} \left( \frac{1}{2x} \right)\]</p> <p>Étant donné que \(\frac{1}{2x}\) tend vers 0 lorsque \(x\) tend vers l'infini :</p> <p>\[\lim_{x \to \infty} \left( \frac{1}{2x} \right) = 0\]</p> <p>On obtient donc :</p> <p>\[2 \cdot 0 = 0\]</p> <p>La réponse est donc 0.</p>
Limit Calculation at Infinity
\[ \lim_{{x \to \infty}} \frac{{2x + 1}}{{4x + 5}} = \frac{{\frac{{2x}}{{x}} + \frac{{1}}{{x}}}}{{\frac{{4x}}{{x}} + \frac{{5}}{{x}}}} \] \[ = \frac{{2 + \frac{{1}}{{x}}}}{{4 + \frac{{5}}{{x}}}} \] \[ = \frac{{2}}{{4}} \quad \text{quand } x \to \infty \] \[ = \frac{1}{2} \]
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