Quiz 26B Solution Guyang Cao December 12 2024 1 Question 1 2 Y 0 Y 1 1 1 0 81 0 0 9 and E 1 0 Y 2 0 1 by the formula of Euler s method 11 10 1 and therefore the integer part of 1000E is 9 0 81 By the formula of Trapezoid s method 1 1 0 9095 4 09 10 4 which means Solution For the first blank since Y0 y 1 1 Y 1 1 0 9 1 Y1 Y0 hY which is the answer of the first blank 1 Y1 For the second blank Y1 0 9 and Y 0 9095 and E1 1 Y1 Y0 h the integer part of 10000E1 is 4 which is the answer of the second blank For the third blank since Y0 y 2 1 Y1 Y0 hY integer part of 10000E2 is 11 or 12 which is the answer of the third blank For the last blank Y1 0 475 and Y Y1 Y0 h which means the integer part of 10000E1 is 0 which is the answer of the last blank 2 1 4 by the formula of Euler s method 2 1 0 475 1 19 10 3 and therefore the 2 1 0 22619 By the formula of Trapezoid s method 0 4761905 and E3 1 2 1 0 4761905 2 38 10 8 0 Y0 4 0 475 and E2 1 1 0 5 0 25 0 22619 2 0 1 1 1 0 475 0 Y 2 Y 0 1 2 Y 20 20 2 1 2 Question 2 30 1 1 and Y 1 21 0 834712 1 1 1 21 Y2 Y0 2hY 1 1 0 2 1 0 833249 and E1 1 Solution For the first blank when using the formula of modified Euler s method we should notice that we have access to the true Y1 1 1 21 0 83471 and 1 2 0 83471 1 37 10 3 and therefore the integer part of 10000E is 13 or 14 which is the E 1 answer of the first blank For the second blank by the formula of Simpson s method Y2 Y0 h 1 4 of 105 E1 is 8 or 9 which is the answer of the second blank For the third blank we notice that we have access to the true Y1 1 the formula of modified Euler s method Y2 Y0 2hY E2 1 answer of the third blank For the last blank by the formula of Simpson s method Y2 Y0 h 0 25 4 teger part of 106 E3 is 1 or 2 which is the answer of the last blank 2 12 by 2 12 0 4546485 and 2 2 0 475 1 03 10 4 and therefore the integer part of 105 E2 is 10 or 11 which is the 1 Y 0 4 Y 3 Y 2 1 1 2 0 833249 8 43 10 5 which means the integer part 3 Y 0 4 Y 1 Y 2 1 1 2 0 833249 1 72 10 6 which means the in 0 45454374 and E1 1 2 0 2 1 1 1 2 12 0 4546485 2 1 and Y 1 1 30 2 2 2