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Home Question Bank Math Calculus Archive 2024 November 06

Calculus Questions from Nov 06,2024

Browse the Calculus Q&A Archive for Nov 06,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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b) \( \int\left(\frac{9 x^{4}}{6}-\frac{3 x^{3}}{7}+\frac{7 x^{2}}{5}-\frac{8 x}{9}+\frac{5}{8}\right) d x \) a. \( \quad f(x)=5 x \sqrt{25-x^{2}} \) find \( \frac{d y}{d x} \). \( \mathbb{T} y=e^{x^{x^{e}}}+e^{x^{e^{x}}} \) 4. a) Bestimmen Sie die Funktionsgleichung einer Funktion dritten Grades, deren Graph durch den Ursprung verläuft. Die Gleichung der Wendetangente an der Stelle \( x=2 \) lautet \( t(x)=-2 x+8 \). b) Bestimmen Sie die Funktionsgleichung einer Funktion dritten Grades, deren Graph die \( x \)-Achse an der Stelle \( x=-1 \) berührt und einen Extrempunkt \( E(1 \mid 1) \) aufweist. c) Bestimmen Sie die Funktionsgleichung einer ganzrationale Funktion möglichst niedrigen Grades, deren Graph punktsymmetrisch zum Koordinatenursprung ist und den Sattelpunkt S(1|1) hat. \( f(x)=x^{2}-x-1 \). On pose \( x_{0}=2 \). a. Résoudre l'équation \( x^{2}-x-1=0 \). On note \( \Phi \) la solution positive de cette équation. b. Montrer que pour tout entier naturel \( n \), on a: \( x_{n+1}=\frac{x_{n}^{2}+1}{2 x_{n}-1} \). c. Soit \( g \) la fonction définie sur \( [1 ;+\infty[ \) par \( g(x)=\frac{x^{2}+1}{2 x-1} \). Étudier les variations de la fonction \( g \). \( s = 2 \pi \int _ { 0 } ^ { 8 } x ^ { 1 / 3 } \sqrt { 1 + ( \frac { 1 } { 3 x ^ { 2 } / 3 } ) ^ { 2 } } \) \( s = 2 \pi \int _ { 0 } ^ { 8 } x ^ { 1 / 3 } \sqrt { 1 + ( \frac { 1 } { 3 x ^ { 2 } } ) ^ { 2 } } \) 89. Si \( f(x)=\sqrt{x}+\frac{1}{\sqrt{x}} \) evalúe la expresión \( \frac{x-1}{2 x \sqrt{x}}-f^{\prime}(x) \) 87. Encuentre todos los puntos sobre la curva \[ y=x^{2}-5 x+3 \] en los que la pendiente es 1. A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at the rate of 4 feet per second. Find the rate at which the area is changing at the instant the radius is 13 feet. When the radius is 13 feet, the area is changing at approximately \( \square \) square feet per second. (Round to the nearest thousandth as needed.)
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