Encuentre el valor asociado \( k \) de la siguiente razón: \( 23: 10 \) (veintitrés sobre diez)

1. Which event convinced people that James Monroe's presidency was ushering in an "Era of Good Feelings?" Monroe's opening of the American west to settlement by immigrants from any European nation Monroe's support of Henry Clay as Speaker of the House after facing Clay as an election opponent government spending on internal improvements such as new roads Monroe's attempts to promote national unity by traveling around New England to talk with important Federalists

Apply the three-step method to compute the derivative of \( f(x)=7 x^{3} \) \( f^{\prime}(x)=\square \)

1. \( \int x^{3} e^{x^{2}} d x=\quad \) (Sugerencia: Sea \( x^{2}=\mathrm{t} \) ) 2. \( \int t^{3} e^{2 t} d t= \) 3. \( \int \frac{500 \ln (x+20)}{(x+20)^{2}} d x= \) 4. \( \int x^{3} \ln x d x= \) 5. Verificar los puntos 1 y 2 por el método tabular. Nota: El taller tiene un valor de 15 puntos. > Enviar a campus virtual en asignaciones. D Elegir un estudiante del grupo para enviar el producto.

Find \( y^{\prime \prime} \) \[ y=x^{\frac{4}{5}}+4 x \]

\( u_{0}=1 \) et pour tout \( n \geq 0, u_{n+1}=\sum_{i=0}^{n} 2^{n-i} u_{i} \)