A slope eld is shown for which of the following differential equations? (10 points) ___\\\\5y\\\\ l l l l l //// fl.\" Q 6. (07.03 MC) Let y = f (x) be the solution to the differential equation f'(x) = 2xy with the initial condition f (1) = 2. What is the approximation for f (2) if Euler's method is used with two steps of equal length? (10 points) O 75 10 O 20 O 963/ 2xy which of the following is the solution to the differential equation : 2 x + 3 , with the initial condition y(3) = 6? (10 points) 0 y=|n|x2+3l O y=|n|x2+1l+ln(4) O y=%x2+3 Let y = f(x) be the particular solution to the differential equation =-3xy , with the initial condition f(1) = 1. Which of the following gives an expression for f(x) and the domain for which the solution is valid? (10 points) dx O f ( x ) = 1 for ( -oo , - (2 , and (2 0. ) = V 3x 2 -2 Of( x ) = 1 for ( -0o, - 2 ) and ( 12,00 ) = V3x2 - 2 f ( x ) = - 1 for ( -oo , - ( 2 , and ( 3 . . ) - V3x2 - 2 Of( x ) = - 1 for ( -oo , - V2 ) and ( 2, 00 ) V3x2 -22 The number of guests at a theme park can be modeled by function P(t) where t is measured in hours. P is a solution to the logistic differential equation d_p : 5- P where P(0) = 2,500. What is the greatest rate of change of the number of guests at d! 4 60000 ' the park, per hour? (10 points) O 511 guests per hour 0 938 guests per hour 0 2,500 guests per hour 0 7,500 guests per hour