(a) Verify that y = tan (x + c) is a one-parameter family of solutions of the differential equation y' = 1 + y².
(b) Since f(x, y) = 1 + y² and ∂f/∂y = 2y are continuous everywhere, the region R can be taken to be the entire xy-plane. Use the family of solutions in part (a) to find an explicit solution of the first-order initial-value problem y' = 1 + y², y(0) = 0. Even though xₒ = 0 is in the interval (-2, 2), explain why the solution is not defined on this interval.

Aprofessional hockey team has noticed that, over the past several seasons, as the number of wins increases, the total number of hot dogs sold at the concession stands increases. the hockey team concludes that winning makes people crave hot dogs. what is wrong with the hockey team's conclusion? a) it does not take into account the attendance during each season. b) it does not take into account the number of hamburgers sold during each season. c) it does not take into account the number of concession stands in the hockey arena. d) it does not take into account the number of seasons the hockey team has been in existence.