Si la función de velocidad es \( v(t) = 3t^2 - 4t + 1 \), ¿cuál es la acumulación del cambio entre \( t = 0 \) y \( t = 5 \)?

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. \( f(x)=\left(8 x^{2}+2 x-3\right)\left(5 x^{3}+2\right) \)

The brain mass of a fetus can be estimated using the total mass of the fetus by the function \( b=0.22 \mathrm{~m}^{0.87} \), where m is the mass of the fetus (in grams) and b is the brain ma: grams). Suppose the brain mass of a \( 21-\mathrm{g} \) fetus is changing at a rate of 0.26 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.)

\( 1 \leftarrow \) 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.)

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

The brain mass of a fetus can be estimated using the total mass of the fetus by the function \( b=0.22 \mathrm{~m}^{0.87} \), where m is the mass of the fetus (in grams) and \( b \) is the brain mass 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, \( \frac{\mathrm{dm}}{\mathrm{dt}} \).