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Home Question Bank Math Calculus Archive 2025 January 07

Calculus Questions from Jan 07,2025

Browse the Calculus Q&A Archive for Jan 07,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( e ^ { x } \geq 1 + x \) 2 Limite en I'infini d'un polynōme ou d'une fraction rationnelle Calculer les limites des fonctions suivantes, et préciser lorsque la courbe représentative de \( f \) (botée \( \left(\mathcal{C}_{f}\right) \) ) wimet une asymptote horizontale. 1. \( f(x)=x^{3}-2 x+3 \), en \( +\infty \). 2. \( f(x)=\frac{x+3}{2 x-1} \) en \( -\infty \). 3. \( f(x)=x^{4}+x \) en \( -\infty \). 4. \( f(x)=\frac{x^{2}-2}{2 x+3} \) en \( -\infty \). 5. \( f(x)=\frac{2 x-5}{x+x^{3}} e x+\infty \). 6. \( f(x)=\frac{4-2 x^{4}}{x^{2}(x+1)^{2}} \) en \( -x \). Aide 7. \( f(x)=\frac{(3 x+1)^{2}}{(2 x-3)^{3}} \mathrm{en}+\infty \). Réponses - I parte. Resmalve las sig, derivados de funciomes truganoret Iuvarses (1) \( f(x)=\operatorname{sen}^{-1}\left(\sqrt{e^{x^{3}}}\right) f^{\prime}(x) \) 3. Resolva os problemas de Cauchy: a) (4) \( \left(\sin x^{2}+3 y^{2}\right) y^{\prime}+2 x y \cos x^{2}=0, \quad y\left(\sqrt{\frac{\pi}{6}}\right)=1 \) b) \( (4) x y^{\prime}-y-x^{2}(2 x-1)=0, \quad y(2)=6 \) Find the area between the curves \( y = x^2 \) and \( y = 4 - x^2 \) from \( x = -2 \) to \( x = 2 \). \( \sum _{k=1}^{n}(\frac{n+k}{n^{2}+k^{2}}) \) \( \sum _{k=1}^{n}(\frac{n+k}{n^{2}+k^{2}}) \) Evia de Ejgracies - I parte. Resmalve las sig, derivodis Se funcianes tiganoret. Juvarses (1) \( f(x)=\operatorname{sen}^{-1}\left(\sqrt{e^{x^{3}}}\right) f^{\prime}(x) \) Encuentra el volumen del sólido formado al rotar la región bajo la curva \( y = e^{x} \) desde \( x = 0 \) hasta \( x = 2 \) en torno al eje horizontal que pasa por \( y = -1 \). \( \lim _ { x \rightarrow \sum ^ { e ^ { - 1 } } } x + \frac { 1 } { 1 + \ln x } - 1 \)
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