2. Llene la casilla en blanco con la letra \( \mathbf{F} \) (Falso) o \( \mathbf{V} \) (Verdadero) según sea el caso. Justifique. (a) (4 puntos) \( \square \) Si \( f(x)=\int_{-2}^{x} \frac{1}{t+3} d t \), donde \( x>-2 \), entonces \( f^{\prime}(7)=1 / 10 \) (b) (4 puntos) \( \square \lim _{n \rightarrow \infty} \sum_{i=1}^{n} \sin \left(\frac{2 i}{n}\right) \frac{2}{n}=\int_{0}^{2} \sin x d x \) (c) (2 puntos) \( \square \int_{-\pi}^{\pi} \sin ^{13} x d x=0 \)

\( 1 \leftarrow \) 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.)

\( d y ( d x - ( 1 - x ) y ^ { 2 } = ( 2 x - 1 ) y - x \)

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

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, \( \frac{\mathrm{dm}}{\mathrm{dt}} \).

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.)