Parsons Luna
11/30/2023 · Junior High School

Sea S el sólido descrito de la forma siguiente: \[ \delta=\left\{(x ; y ; z) \in \mathbb{R}^{3}: 0 \leq x \leq 2,\left[x^{2} \leq y \leq 4,0 \leq z \leq 2-x\right]\right. \] a) Graficar el sólido S . b) Describir el sólido S de una forma distinta. \[ x=0 \]

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### a) Graficar el sólido \( S \) Para graficar el sólido \( S \), considera las restricciones: - \( 0 \leq x \leq 2 \) - \( x^2 \leq y \leq 4 \) - \( 0 \leq z \leq 2 - x \) El sólido es un "cubo" truncado en la parte superior por la parábola y en la parte frontal por el plano inclinado. ### b) Describir el sólido \( S \) de otra manera El sólido \( S \) tiene una base en el plano \( z = 0 \), limitada por \( y = x^2 \) y \( y = 4 \). La altura en cada punto de la base es \( z = 2 - x \), descendiendo desde \( z = 2 \) en \( x = 0 \) hasta \( z = 0 \) en \( x = 2 \).

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