Pre-Calc Homework Solutions 274

Pre-Calc Homework Solutions 274 - 1.0572 1.0546 0.0026 2...

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9. To find the approximate values, set y 1 5 2 y 1 sin x and use EULERT with initial values x 5 0 and y 5 0 and step size 0.1 for 10 points. The exact values are given by y 5 } 1 5 } ( e 2 x 2 2 sin x 2 cos x ). 10. To find the approximate values, set y 1 5 x 2 y and use EULERT with initial values x 5 0 and y 52 2 and step size 0.1 for 10 points. The exact values are given by y 5 x 2 1 2 e 2 x . 11. To find the approximate values, set y 1 5 2 y ( x 1 1) and use IMPEULT with initial values x 52 2 and y 5 2 and step size 0.1 for 20 points. The exact values are given by y 5 2 e x 2 1 2 x . 274 Section 6.6 x y 12 improved Euler y (exact) Error 2 2 2 2 0 2 1.9 1.6560 1.6539 0.0021 2 1.8 1.3983 1.3954 0.0030 2 1.7 1.2042 1.2010 0.0032 2 1.6 1.0578 1.0546 0.0032 2 1.5 0.9478 0.9447 0.0031 2 1.4 0.8663 0.8634 0.0029 2 1.3 0.8077 0.8050 0.0027 2 1.2 0.7683 0.7658 0.0025 2 1.1 0.7456 0.7432 0.0024 2 1.0 0.7381 0.7358 0.0023 2 0.9 0.7455 0.7432 0.0023 2 0.8 0.7682 0.7658 0.0024 2 0.7 0.8075 0.8050 0.0024 2 0.6 0.8659 0.8634 0.0025 2 0.5 0.9473 0.9447 0.0026 2 0.4
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Unformatted text preview: 1.0572 1.0546 0.0026 2 0.3 1.2036 1.2010 0.0026 2 0.2 1.3976 1.3954 0.0022 2 0.1 1.6553 1.6539 0.0014 1.9996 2 0.0004 x y (Euler) y (exact) Error 2 2 2 2 0.1 2 1.8000 2 1.8048 0.0048 0.2 2 1.6100 2 1.6187 0.0087 0.3 2 1.4290 2 1.4408 0.0118 0.4 2 1.2561 2 1.2703 0.0142 0.5 2 1.0905 2 1.1065 0.0160 0.6 2 0.9314 2 0.9488 0.0174 0.7 2 0.7783 2 0.7966 0.0183 0.8 2 0.6305 2 0.6493 0.0189 0.9 2 0.4874 2 0.5066 0.0191 1.0 2 0.3487 2 0.3679 0.0192 x y (Euler) y (exact) Error 0.1 0.0053 0.0053 0.2 0.0100 0.0229 0.0129 0.3 0.0318 0.0551 0.0233 0.4 0.0678 0.1051 0.0374 0.5 0.1203 0.1764 0.0561 0.6 0.1923 0.2731 0.0808 0.7 0.2872 0.4004 0.1132 0.8 0.4090 0.5643 0.1553 0.9 0.5626 0.7723 0.2097 1.0 0.7534 1.0332 0.2797...
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