a) (1.25 points) Calculate, if they exist, the value of the following limits: a.1) $(0.5$ points) $\lim _ { x \rightarrow 0 } \frac { x ^ { 2 } ( 1 - 2 x ) } { x - 2 x ^ { 2 } - \operatorname { sen } x }$ a.2) (0.75 points) $\lim _ { x \rightarrow \infty } \frac { 1 } { x } \left( \frac { 3 } { x } - \frac { 2 } { \operatorname { sen } \frac { 1 } { x } } \right)$ (Hint: use the change of variable $t = 1 / x$ where necessary). b) (1.25 points) Calculate the following integrals: b.1) (0.5 points) $\int \frac { x } { x ^ { 2 } - 1 } d x$ b.2) (0.75 points) $\int _ { 0 } ^ { 1 } x ^ { 2 } e ^ { - x } d x$
a) (1.25 points) Calculate, if they exist, the value of the following limits:
a.1) $(0.5$ points) $\lim _ { x \rightarrow 0 } \frac { x ^ { 2 } ( 1 - 2 x ) } { x - 2 x ^ { 2 } - \operatorname { sen } x }$
a.2) (0.75 points) $\lim _ { x \rightarrow \infty } \frac { 1 } { x } \left( \frac { 3 } { x } - \frac { 2 } { \operatorname { sen } \frac { 1 } { x } } \right)$
(Hint: use the change of variable $t = 1 / x$ where necessary).
b) (1.25 points) Calculate the following integrals:
b.1) (0.5 points) $\int \frac { x } { x ^ { 2 } - 1 } d x$
b.2) (0.75 points) $\int _ { 0 } ^ { 1 } x ^ { 2 } e ^ { - x } d x$