Estas preguntas se desarrollan a partir de un enunciado, problema o contexto, y ofrecen cuatro opciones de respuesta. Solo una de es opciones es la correcta, por lo que debes elegir la opción que responda correctamente al ítem planteado. Enunciado: ¿Cual es el límite de la siguiente función? \( \lim _{x \rightarrow 0} \frac{\operatorname{Sen}(2 x)+\operatorname{Sen}(3 x)}{\operatorname{Sen}(4 x)+\operatorname{Sen}(5 x)} \) \( \frac{5}{3} \) \( \frac{3}{6} \) \( \frac{5}{9} \)

What is the average distance between the parabola \( y=7 x(18-x) \) and the \( x \)-axis on the interval \( [0,18] \) ? The average distance is (Type an integer, proper fraction, or mixed number)

The elevation of a path is given by \( f(x)=x^{3}-6 x^{2}+4 \), where \( x \) measures horizontal distances. Draw a graph of the elevation function and find its average value for \( 0 \leq x \leq 4 \).

The function \( h(t)=1+4 t-1.86 t^{2} \) models the height of a rock thrown upward on the planet Mars, where \( h(t) \) is height in metres and \( t \) is time in seconds. Use a graph to determine a) the maximum height the rock reaches b) how long the rock will be above the surface of Mars

\( y ^ { \prime \prime } + y = x ^ { 3 } + 1 \)

Find or approximate the point(s) at which the given function equals its average value on the given interval. \( f(x)=1-\frac{x^{2}}{a^{2}},[0, a] \) where a is a positive real number The point(s) at which \( f(x) \) equals its average value is/are (Type an exact answer, using radicals as needed Use a comma to separate answers as needed.)