spain-selectividad 2023 QB.2

spain-selectividad · Other · selectividad__madrid_matematicas-II_extraordinaria 2 marks Areas Between Curves Multi-Part Free Response with Area, Volume, and Additional Calculus

Given the functions
$$f ( x ) = 2 + 2 x - 2 x ^ { 2 } \text { and } g ( x ) = 2 - 6 x + 4 x ^ { 2 } + 2 x ^ { 3 } ,$$
find:\ a) (1 point) Study the differentiability of $h ( x ) = | f ( x ) |$.\ b) (1.5 points) Find the area of the region bounded by the curves\ $y = f ( x ) , y = g ( x ) , x = 0$ and $x = 2$.

Given the functions

$$f ( x ) = 2 + 2 x - 2 x ^ { 2 } \text { and } g ( x ) = 2 - 6 x + 4 x ^ { 2 } + 2 x ^ { 3 } ,$$

find:\
a) (1 point) Study the differentiability of $h ( x ) = | f ( x ) |$.\
b) (1.5 points) Find the area of the region bounded by the curves\
$y = f ( x ) , y = g ( x ) , x = 0$ and $x = 2$.

Paper Questions

QA.1 QA.2 QA.3 QA.4 QB.1 QB.2 QB.3 QB.4