Given the real function of a real variable defined on its domain as $f ( x ) = \left\{ \begin{array} { l l l } \frac { x ^ { 2 } } { 2 + x ^ { 2 } } & \text { if } & x \leq - 1 \\ \frac { 2 x ^ { 2 } } { 3 - 3 x } & \text { if } & x > - 1 \end{array} \right.$, find:\ a) ( 0.75 points) Study the continuity of the function on $\mathbb{R}$.\ b) (1 point) Calculate the following limit: $\lim _ { x \rightarrow - \infty } f ( x ) ^ { 2 x ^ { 2 } - 1 }$.\ c) (0.75 points) Calculate the following integral: $\int _ { - 1 } ^ { 0 } f ( x ) d x$.
Given the real function of a real variable defined on its domain as $f ( x ) = \left\{ \begin{array} { l l l } \frac { x ^ { 2 } } { 2 + x ^ { 2 } } & \text { if } & x \leq - 1 \\ \frac { 2 x ^ { 2 } } { 3 - 3 x } & \text { if } & x > - 1 \end{array} \right.$, find:\
a) ( 0.75 points) Study the continuity of the function on $\mathbb{R}$.\
b) (1 point) Calculate the following limit: $\lim _ { x \rightarrow - \infty } f ( x ) ^ { 2 x ^ { 2 } - 1 }$.\
c) (0.75 points) Calculate the following integral: $\int _ { - 1 } ^ { 0 } f ( x ) d x$.