Since f(x, y) = 1 + y2 and ∂f/∂y = 2y are continuous everywhere, the region r in theorem 1.2.1 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. y = even though x0 = 0 is in the interval (−2, 2), explain why the solution is not defined on this interval. since tan(x) is discontinuous at x = ± , the solution is not defined on (−2, 2).

Afootball is throw by a quarterback to a receiver

Aparticular telephone number is used to receive both voice calls and fax messages. suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. (a) what is the expected number of calls among the 25 that involve a fax message?

Sara has been reading about different types of financial grants, including federal pell grants, academic competitiveness grants, smart grants, and teach grants. which statement about these grants is true? filling out a fafsa will not her apply for these grants. she will not have to pay back any funds she receives from these grants. these grants only go to students with less than a 3.0 gpa. she will have to pay back all the funds she receives from these grants.