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3. Il ie esumate Tor an negrai using four trapezoids is 26.35 and the estimate using eight trapez0ids is 19.33, then the error in the estimate using two trapeziods is (a) (b) 6.469 10.667 0.267 9.366 (e) none of the above 6. The following quadratures are open rules that can be applied to integrands with singular endpoints (a) basic and compound trapezoidal rules Gauss quadratures (c) Romberg integration based on the compound Trapezoidal rule Romberg integration based on the compound Midpoint rule none of the above (e) 7. An 8-point Gauss quadrature rule will (a) exactly integrate a 8th order trigonometric function (b) exactly integrate a 13th order exponential function exactly integrate a 15th order polynomial function (d) exactly integrate a 18th order polynomial function none of the above (e) 8. To implement a Gauss-Legendre rule for interval [-1,1 is given by (a) x(E) 3.5 x(E) 1.75 E +3.75 (c) x(E3.5 1.5 (d) x(E) 1.5 E +3.5 (e) x(E) 25.5 integral over the range [a,b] [2, 5.5] the linear map onto the 9.The methods we developed for the numerical solution of the ODE for initial problems had global truncation errors that were one order less than the local truncation error when applied to a 3rd order ODE led to solving three coupled first order ODE's had global truncation errors that were one order more than the local truncation error when combined with a error estimate could be used with adaptive time stepping none of the above 10. Using reduction of order applied to an initial value problem governed by two coupled 4th order ODE's to be solved by leads to a system of (a) two coupled first order ODE's eight coupled first order ODE's (c) four independent first order partial differential equations (d) four coupled algebraic equations none of the above 3. Il ie esumate Tor an negrai using four trapezoids is 26.35 and the estimate using eight trapez0ids is 19.33, then the error in the estimate using two trapeziods is (a) (b) 6.469 10.667 0.267 9.366 (e) none of the above 6. The following quadratures are open rules that can be applied to integrands with singular endpoints (a) basic and compound trapezoidal rules Gauss quadratures (c) Romberg integration based on the compound Trapezoidal rule Romberg integration based on the compound Midpoint rule none of the above (e) 7. An 8-point Gauss quadrature rule will (a) exactly integrate a 8th order trigonometric function (b) exactly integrate a 13th order exponential function exactly integrate a 15th order polynomial function (d) exactly integrate a 18th order polynomial function none of the above (e) 8. To implement a Gauss-Legendre rule for interval [-1,1 is given by (a) x(E) 3.5 x(E) 1.75 E +3.75 (c) x(E3.5 1.5 (d) x(E) 1.5 E +3.5 (e) x(E) 25.5 integral over the range [a,b] [2, 5.5] the linear map onto the 9.The methods we developed for the numerical solution of the ODE for initial problems had global truncation errors that were one order less than the local truncation error when applied to a 3rd order ODE led to solving three coupled first order ODE's had global truncation errors that were one order more than the local truncation error when combined with a error estimate could be used with adaptive time stepping none of the above 10. Using reduction of order applied to an initial value problem governed by two coupled 4th order ODE's to be solved by leads to a system of (a) two coupled first order ODE's eight coupled first order ODE's (c) four independent first order partial differential equations (d) four coupled algebraic equations none of the above