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Home Question Bank Math Calculus Archive 2024 December 19

Calculus Questions from Dec 19,2024

Browse the Calculus Q&A Archive for Dec 19,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Se quiere construir una caja sin tapa a partir de una hoja de cartón de \( 24 \times 36 \mathrm{~cm} \). ¿Cuóntos centínetros debes cortar en cada esquina para obtener el máximo volumen? Exercices de fixation betermine chacune des limites suivantes: 1) \( \lim _{x \rightarrow 0}(x+\ln x) \); 2) \( \lim _{x \rightarrow+\infty}(x+\ln x) \); 3) \( \lim _{x \rightarrow+\infty}(x-\ln x) \) 6 Détermine chacune des limites suivantes: 1) \( \lim _{x \rightarrow 0}(x+\ln x) \) : 2) \( \lim _{x \rightarrow+\infty}(x+\ln x) \) 3) \( \lim _{x \rightarrow+\infty}(x-\ln x) \) For what values of the numbers \( a \) and \( b \) does the function \[ f(x)=a x e^{b x^{2}} \] have the maximum value \( f(5)=1 \) ? \( b=\square \) [-/1 Points] DETAILS MY NOTES SOALCET9 4.3.083.MI. Find a cubic function \( f(x)=a x^{3}+b x^{2}+c x+d \) that has a local maximum value of 4 at \( x=-2 \) and a local minimum value of 0 at \( x=1 \). \( f(x)=\square \) Given that \( f(x)=x^{2}+\sqrt{x+1} \). Find \( \int_{0}^{3} f^{\prime}(x) d x \) Given that \( f(x)=x^{2}+\sqrt{x+1} \). Find \( \int_{0}^{3} f(x) d x \) \( \int _ { - 2 } ^ { 3 } \frac { 1 } { x ^ { 4 } } d \) Si \( f(x)=\frac{(x+1)^{2}}{x^{2}+1} \), entonces la función \( f(x) \) es cóncava hacia arriba en: a. \( (-\infty,-\sqrt{3}) \cup(\sqrt{3},+\infty) \) b. \( (-\sqrt{3}, \sqrt{3}) \) c. \( (-\sqrt{3}, 0) \cup(\sqrt{3},+\infty) \) d. \( (\sqrt{3},+\infty) \) ¿Cuál es la ecuación de la recta tangente a la curva \( f(x)=-x^{2}+1 \) en el punto de abscisa \( x=-2 \) ? \( \begin{array}{l}\text { a. } y=-2 x+1 \\ \text { b. } y-3=4(x+2) \\ \text { c. } y-1=2(x+2) \\ \text { d. } y=4 x+5\end{array} \)
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