spain-selectividad 2022 QA.2

spain-selectividad · Other · selectividad__madrid_matematicas-II 2.5 marks Indefinite & Definite Integrals Definite Integral Evaluation (Computational)

Let the function $f ( x ) = \left\{ \begin{array} { l l l } x ^ { 3 } e ^ { - 1 / x ^ { 2 } } & \text { if } & x \neq 0 \\ 0 & \text { if } & x = 0 \end{array} \right.$ a) (1 point) Study the continuity and differentiability of $f ( x )$ at $x = 0$. b) ( 0.5 points) Study whether $f ( x )$ presents any type of even or odd symmetry. c) (1 point) Calculate the following integral: $\int _ { 1 } ^ { 2 } \frac { f ( x ) } { x ^ { 6 } } d x$

Let the function $f ( x ) = \left\{ \begin{array} { l l l } x ^ { 3 } e ^ { - 1 / x ^ { 2 } } & \text { if } & x \neq 0 \\ 0 & \text { if } & x = 0 \end{array} \right.$\\
a) (1 point) Study the continuity and differentiability of $f ( x )$ at $x = 0$.\\
b) ( 0.5 points) Study whether $f ( x )$ presents any type of even or odd symmetry.\\
c) (1 point) Calculate the following integral: $\int _ { 1 } ^ { 2 } \frac { f ( x ) } { x ^ { 6 } } d x$

Paper Questions

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