João Augusto

 Find the derivative of the function  f ( x ) = 2 x 3 − 4 x + 1 x 2 + 1 f(x) = \frac{2x^3 - 4x + 1}{x^2 + 1} Options: A) 6 x 2 ( x 2 + 1 ) − ( 2 x 3 − 4 x + 1 ) ( 2 x ) ( x 2 + 1 ) 2 \frac{6x^2(x^2 + 1) - (2x^3 - 4x + 1)(2x)}{(x^2 + 1)^2} ​ B) ( 6 x 2 − 4 ) ( x 2 + 1 ) − ( 2 x 3 − 4 x + 1 ) ( 2 x ) ( x 2 + 1 ) 2 \frac{(6x^2 - 4)(x^2 + 1) - (2x^3 - 4x + 1)(2x)}{(x^2 + 1)^2} ​ C) ( 6 x 2 − 4 ) ( x 2 + 1 ) − ( 2 x 3 − 4 x + 1 ) ( 2 ) ( x 2 + 1 ) 2 \frac{(6x^2 - 4)(x^2 + 1) - (2x^3 - 4x + 1)(2)}{(x^2 + 1)^2} D) ( 6 x 2 − 4 ) ( x 2 + 1 ) − ( 2 x 3 − 4 x + 1 ) ( x ) ( x 2 + 1 ) 2 \frac{(6x^2 - 4)(x^2 + 1) - (2x^3 - 4x + 1)(x)}{(x^2 + 1)^2} ​ E) None of the above​ Original idea by: João Augusto Ferreira de Moura

  Given the undirected graph bellow: What is the distance from A to all nodes in this graph if we use a BFS algorithm starting from A? a) A - 0, B - 1, C - 2, D - 1, E - 2, F - 3, H - 4, G - 0 b) A - 0, B - 1, C - 2, D - 1, E - 2, F - 2, H - 3, G - 4 c) A - 0, B - 1, C - 2, D - 1, E - 2, F - 2, H - 3, G - Null d) A - 0, B - 1, C - 2, D - 1, E - 2, F - 2, H - 3, G - Null e) None of the above