Solucionario Calculo Una Variable Thomas Finney Edicion 9 179 File

[ 3x^2 = 4R^2 \quad\Longrightarrow\quad x = \frac{2R}{\sqrt{3}}. ]

Maya wrote the result in bold, underlined it, and added a small smiley face next to it—her personal signature of triumph. The next morning, the professor walked into the seminar room, a stack of papers in his hand. He asked the class to volunteer a solution for Exercise 179. Maya’s hand rose, heart thudding like a metronome. He asked the class to volunteer a solution for Exercise 179

Simplifying gave

When she stood, the room fell silent. She described the geometry, the substitution of , the elegant reduction to a single‑variable function, and the calculus steps that led to the cube. She finished with the final expression (\displaystyle V_{\max}= \frac{8R^3}{3\sqrt{3}}) and a quick sketch of the inscribed cube inside the sphere. She described the geometry, the substitution of ,

Setting the numerator to zero (the denominator never vanished inside the feasible interval) produced She described the geometry

Discarding the trivial solution (x = 0) (which gave zero volume), she solved

[ V(x) = x^2 \cdot y = x^2 \cdot 2\sqrt{R^2 - \frac{x^2}{2}} = 2x^2\sqrt{R^2 - \frac{x^2}{2}} . ]