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Estudos Gerais05/21/2025

1. Calcule o comprimento do gráfico da função dada. a) $y = ...

  1. Calcule o comprimento do gráfico da função dada. a) y=23x32,0x1y = \frac{2}{3}x^{\frac{3}{2}}, 0 \leq x \leq 1 b) y=43x+3,0y2y = \frac{4}{3}x+3, 0 \leq y \leq 2. c) y=lnx,1xey=\ln{x}, 1\leq x \leq e d) y=x,14x34y = \sqrt{x}, \frac{1}{4} \leq x \leq \frac{3}{4}. f) y=ex,0x1y=e^{x}, 0\leq x \leq 1 g) y=ex+ex2,0x1y=\frac{e^{x}+e^{-x}}{2}, 0\leq x \leq 1.

Apenas F e G. Faça um cálculo simples e objetivo

1. Calcule o comprimento do gráfico da função dada.
a) $y = \frac{2}{3}x^{\frac{3}{2}}, 0 \leq x \leq 1$
b) $y = \frac{4}{3}x+3, 0 \leq y \leq 2$.
c) $y=\ln{x}, 1\leq x \leq e$
d) $y = \sqrt{x}, \frac{1}{4} \leq x \leq \frac{3}{4}$.
f) $y=e^{x}, 0\leq x \leq 1$
g) $y=\frac{e^{x}+e^{-x}}{2}, 0\leq x \leq 1$.
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