3) Sea \( F(x)=\frac{x^{3}+3 x-x^{2}-3}{5 x^{2}-5} \quad \) si \( x<1 \) HACLAR \( \lim _{x \rightarrow 1} F(x) \) y \( \lim _{x \rightarrow 0} F(x) \)

\( \int _ { - 1 } f ( x ^ { 2 } - 1 ) d x = \lim _ { n \rightarrow \infty } [ \sum _ { i = 1 } ^ { n } \frac { 3 - ( - 1 ) } { n } \cdot f ( ( - 1 ) + i \cdot \frac { 3 - ( - 1 ) } { n } ) ] \)

El volumen se calcula mediante una integral doble sobre la base del plano (zy) y la alurara \( z(z, y) \). Ya sabemos que lo equación del plano es: \[ z=11-\frac{11 e}{0}-\frac{11 y}{10} . \]

Derivar las siguientes funciones 1. \( f(x)=(4 x+1)(6 x+3) \) 2. \( f(x)=(8-7 t)\left(t^{2}-2\right) \) 3. \( f(x)=\left(3 r^{2}-4\right)\left(r^{2}-5 r+1\right) \) 4. \( f(x)=\left(x^{2}+3 x-2\right)\left(2 x^{2}-x-3\right) \) 5. \( f(x)=\left(8 x^{2}+2 x-3\right)\left(5 x^{3}+2\right) \)

1 The brain mass of a fetus can be estimated using the total mass of the fetus by the function \( \mathrm{b}=0.22 \mathrm{~m}^{0.87} \), where m is the mass of the fetus (in grams) and b is the brain m grams). Suppose the brain mass of a \( 20-\mathrm{g} \) fetus is changing at a rate of 0.23 g per day. Use this to estimate the rate of change of the total mass of the fetus, \( \frac{\mathrm{dm}}{\mathrm{dt}} \). \( \frac{\mathrm{dm}}{\mathrm{dt}}=1.65 \mathrm{~g} \) per day (Round to five decimal places as needed.)

\( 1 \leftarrow \) The brain mass of a fetus can be estimated using the total mass of the fetus by the function \( \mathrm{b}=0.22 \mathrm{~m}^{0.87} \), where m is the mass of the fetus (in grams) and b is the brain mass (in grams). Suppose the brain mass of a 27 - g fetus is changing at a rate of 0.21 g per day. Use this to estimate the rate of change of the total mass of the fetus, \( \frac{\mathrm{dm}}{\mathrm{dt}} \). \( \frac{\mathrm{dm}}{\mathrm{dt}}=\square \mathrm{g} \) per day (Round to five decimal places as needed.)