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Home Question Bank Math Calculus Archive 2024 November 01

Calculus Questions from Nov 01,2024

Browse the Calculus Q&A Archive for Nov 01,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( \frac { d ^ { 2 } y } { d x ^ { 2 } } - 9 y = 0 \) Consider the function \( f(x)=2 x^{2}-12 x-1 \). a. Determine, without graphing, whether the function has a minimum value or a maximum value. b. Find the minimum or maximum value and determine where it occurs. c. Identify the function's domain and its range. a. The function has a b. The minimum/maximum value is c. The domain of \( f \) is \( \square \). It occurs at \( x= \). Type your answer in interval notation.) The range of \( f \) is \( \square \). (Type your answer in interval notation.) \[ \quad \begin{array}{l}\text { Differentiate the function. } \\ y=(3 x-2)^{4}\left(1-x^{5}\right)^{2} \\ \underline{d y}=\square\end{array} \] un máximo local igual a 5 en \( x=-3 \) y un mínimo local igual a 0 en \( x=2 \). 2. Halle el valor de \( c \) de tal forma que la gráfica de \( f(x)=c x^{2}+\frac{1}{x^{2}} \) tenga un punto de inflexión en el punto \( (1, f(x)) \). A plane directly above Denver, Colorado, (altitude 1650 meters) flies to Bismark, North Dakota (altitude 550 meters). It travels at \( 700 \mathrm{~km} / \) hour along a line at 7250 meters above the line joining Donver and Bismark. Bismark is about 850 km in the direction \( 60^{\circ} \) north of east from Denver. Find parametric equations describing the plane's motion. Assume the origin is at sea level beneath Denver, that the \( x \)-axis points east and the \( y \)-axis points north, and that the earth is flat. Measure distances in kilometers and time in hours. \( \vec{r}(t)= \) Differentiate. \( g(x)=\frac{9 x-2}{2 x+3}+x^{3} \) Ejercicio 13. Calcular el área de la región limitada por los gráficos de \( f(x)=\sqrt{x-5} \), \( g(x)=\sqrt{5-x} \) y la recta \( y=2 \). 2) Dada la ecuación diferencial \( y^{\prime}=\frac{2 x}{y} \). Sabiendo que \( y(1)=2 \). Entonces: 33) Si \( y^{2}+2 x y=8 \), montrer que : \( (x+y) \frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x}+\left(\frac{d y}{d x}\right)^{2}=0 \) Encuentra una función vectorial que represente la curva de intersección del paraboloide. \( z=4 x^{2}+2 y^{2} y \) el cilindro \( y=2 x^{2} \). Utilice la variable t como parámetro. \( \mathrm{I}(t)=\langle t \), Nota: Puedes obtener credito parcial en este problema.
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