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Home Question Bank Math Calculus Archive 2024 December 05

Calculus Questions from Dec 05,2024

Browse the Calculus Q&A Archive for Dec 05,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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A equação \( \frac{dy}{dx} = \frac{2y}{x} \) é dada. Determine a solução particular se \( y(2) = 8 \). Evaluate the integral. \[ \int_{\pi / 2}^{0} \cos (\theta) d \theta \] At a sand gravel plant, sand is falling off a conveyor belt and onto a conical pile at the rate of 10 cubic feet per minute. The diameter of the base of the cone is three times the altitude. At what rate is the height of the pile changing when the pile is 15 feet high? None of these. \( 8 /(40577) \mathrm{ft} / \mathrm{min} \) \( 6 /(40577) \mathrm{ft} / \mathrm{min} \) \( 8 /(405) \mathrm{ft} / \mathrm{min} \) 35. Multiple choice 1 point Which of the following are true about a trapezoidal approximation? I. The result will be more accurate as the number of subintervals is increased. II. The trapezoidal rule is always less accurate than using MRAM. III. The trapezoidal approximation method is used when the antiderivative is unknown. I and II I and III 34 Multiple Choice 1 point Use the trapezoidal rule to approximate the area under the curve \( y=\sqrt{x} \) on \( [1,3] \) using 4 subintervals. 2.610 2.797 2.793 2.800 Calcule las derivadas farciciles \( \frac{\partial f}{\partial x} \frac{\partial f}{d y} \frac{\partial f}{d z} \) de las siguientes funciones. \( f(x, y)=\tan \left(x^{2}+2 x y^{2}+y^{3}\right) \) \( \lim F ( x ) = \frac { F ( x + h ) - F ( x } { x } \) 3. Aplicando el criterio de la integral, determine si la serie dada converge o diverge. \( \sum_{n=2}^{\infty} \frac{1}{n(\ln |n|)^{2}} \) If air resistance is neglected, a projectile on Earth shot straight upward with an initial velocity of 46 meters per second will be at a height \( s \) (in meters) given by the function \( s=f(x)=-4.9 x^{2}+46 x \), where \( x \) is the number of seconds elapsed after projection. After how many seconds will it reach its maximum height, and what is th maximum height? It takes \( \square \) second(s) for it to reach its maximum height. (Round to the nearest tenth as needed.) The maximum height obtained is \( \square \) meters. (Round to the nearest tenth as needed.) (4) Encontron Min ó MA' \( x \) en \[ y=\frac{\sqrt{x^{2}+9}}{2}+\frac{5-x}{6} \]
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