Introduction to Maple_________________________________________________________________________________Exercise 2.1 2+2;

IiIl

(3+7+10)*(1000-8)/(900+90+2) - 17;

IiIk

_________________________________________________________________________________Exercise 2.2(a) 6^20 * 15^20 / 9^20;

IjYrKysrKysrKysrIg==

The answer is one followed by 20 zeros, or in other words LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiQtSSVtc3VwR0YkNiUtSSNtbkdGJDYkUSMxMEYnL0YzUSdub3JtYWxGJy1GOzYkUSMyMEYnRj4vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRj5GK0Y+. This is easy to see by hand, because 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 and (6 x 15)/9 is just 10.(b) (10^10 - 1)/99;

IiosLCwsIg==

The answer is 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, or in other words 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. The standard geometric progression formula says that this is the same as 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, or in other words 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.(c) (10^10 - 10 - 9^2)/9^2;

IioqeWNNNw==

To check this by hand, let LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= be the number LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JFEqMTIzNDU2Nzg5RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRi8=. Then 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 and so 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. If we subtract LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= from this the digits mostly cancel and we get 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. Multiply by 9 again to get LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNidGKy1GIzYmLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEiOUYnL0YzUSdub3JtYWxGJy1GPTYkUSIyRidGQC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGQC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGTi8lKXN0cmV0Y2h5R0ZOLyUqc3ltbWV0cmljR0ZOLyUobGFyZ2VvcEdGTi8lLm1vdmFibGVsaW1pdHNHRk4vJSdhY2NlbnRHRk4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0Znbi1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRInhGJ0YvRjItRkk2LVEiK0YnRkBGTEZPRlFGU0ZVRldGWS9GZm5RLDAuMjIyMjIyMmVtRicvRmluRmZvLUY9NiRRIjFGJ0ZARkBGQEZALUZJNi1RIj1GJ0ZARkxGT0ZRRlNGVUZXRlkvRmZuUSwwLjI3Nzc3NzhlbUYnL0ZpbkZfcC1GPTYkUSs5OTk5OTk5OTkwRidGQEZARitGQA==, which is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNidGKy1GIzYkLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEjMTBGJy9GM1Enbm9ybWFsRidGPC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGQC1JI21vR0YkNi1RKCZtaW51cztGJ0ZALyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZLLyUpc3RyZXRjaHlHRksvJSpzeW1tZXRyaWNHRksvJShsYXJnZW9wR0ZLLyUubW92YWJsZWxpbWl0c0dGSy8lJ2FjY2VudEdGSy8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlpGPEZARitGQA==. Rearrange this to get 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 and so 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.(d) (10^9+1)*(10^10 - 10 - 9^2)/9^2;

IjMqeWNNNyp5Y003

Assuming part (c), we have 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 and so 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. These two numbers can be added without any carrying, to giveLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNictSSZtZnJhY0dGJDYoLUYjNiYtSShtZmVuY2VkR0YkNiQtRiM2J0YrLUYjNiQtSSVtc3VwR0YkNiUtSSNtbkdGJDYkUSMxMEYnL0YzUSdub3JtYWxGJy1GRzYkUSI5RidGSi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGSi1JI21vR0YkNi1RIitGJ0ZKLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZYLyUpc3RyZXRjaHlHRlgvJSpzeW1tZXRyaWNHRlgvJShsYXJnZW9wR0ZYLyUubW92YWJsZWxpbWl0c0dGWC8lJ2FjY2VudEdGWC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRmFvLUZHNiRRIjFGJ0ZKRkpGSi1GUzYtUTEmSW52aXNpYmxlVGltZXM7RidGSkZWRllGZW5GZ25GaW5GW29GXW8vRmBvUSYwLjBlbUYnL0Zjb0ZbcC1GPTYkLUYjNipGKy1GIzYkLUZENiVGRkZGRk9GSi1GUzYtUSgmbWludXM7RidGSkZWRllGZW5GZ25GaW5GW29GXW9GX29GYm9GRkZlcC1GIzYkLUZENiVGTC1GRzYkUSIyRidGSkZPRkpGK0ZKRkpGSi1GIzYmRitGaHBGK0ZKLyUubGluZXRoaWNrbmVzc0dGZm8vJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZXEvJSliZXZlbGxlZEdGWC1GUzYtUSI9RidGSkZWRllGZW5GZ25GaW5GW29GXW8vRmBvUSwwLjI3Nzc3NzhlbUYnL0Zjb0Zeci1GIzYmLUZHNiRRMzEyMzQ1Njc4OTAwMDAwMDAwMEYnRkpGUi1GRzYkUSoxMjM0NTY3ODlGJ0ZKRkpGK0ZKRitGSg== = 123456789123456789._________________________________________________________________________________Exercise 2.3The numbers in this exercise are approximations to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUGlGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjI=; in a certain sense, they are actually the best possible approximations. 3 + 1/7;

IyIjQSIiKA==

evalf(%);

JCIrVnImRzkkISIq

3 + 1/(7 + 1/15);

IyIkTCQiJDEi

evalf(%);

JCIrTSU0OjkkISIq

3+1/(7+1/(15 + 1/(1 + 1/293)));

IyInW1Y1IiY6SyQ=

evalf(%);

JCIrYUVmVEohIio=

evalf(Pi);

JCIrYUVmVEohIio=

_________________________________________________________________________________Exercise 2.4 evalf[4997](exp(1));

JCJgY15sbW0xPCJwUShvSCszL0olSClRSWhMbyUpR2BcanAoMzEkPihSNG5yVllqJkh1KHBNamRFMXRJIW9seSQzJ0dbbi5jQGAzS3FNd1dgcmYxJipwbmwyaSJcQCwwImUoemUnSEpKeC5ib2MpZVZsUm91ZmpHKUchMzpLaSNvaz0yIykpZjNNPVVpKipReGcxYGdYc24jPVUhKXBtaGdZLmAoKnk4aipwZGNHInpTRidvM3VfbidmZylHbmB3XGozRDxxYWl2Y2kwQl9GIiopPjciby1UKSlvUHJLazg4JCpRT1NRSz47WVBmWTBwO0kmei5XUUVacShbPUQkKTMlPSVHUEMtRVJrLngocHF3Xyg0cUZsJ0dROypvKydSci9HPih6aDdTRiEpZjpzRS1iVWtEYz1DSFVLeXQkZTBgLkVTYz0oMyUpPSYpKilwN148M1ZeeGRdcWFsImYhSGZ6ZiZ6L1wrPWlQcHIjeS9dUUteTFs2YCtAZ3U9c1gpKVJ0ISllT0QkNCVvR3okeShwRnhRSWYtJ3ppIVFUS2xvXSEqR1IhKlFQRkR0KSl5NydSOVAwb2M7ZWc3Jyl5dEJzN1h6NTVHSnQ9UyUpcFhWVTQ6MSxuTG5AKHlbb0A5ayNHVnlmOUF0Ti0mWy1WKkhUTGt2JWYkXHQmR3RAK1tPPlAjbyxMcUtJQnl0OVczY0ZAZmAoKlwoPTJ1Z0Ftcmk0elgqRzQ8WSFRcUBzKipSSmNaVHU6LEgkcC9JJFFiMUYhRyRbSiRvKSk9LDkkKmZ2SFVcPiIzV3VKOSR5KDM7TDBTV1k6b2pWa2chPTlxeCY9PDk5JjRaTzRoJypRK2cvT0BuZ0lUTi0nSHgieT1xSiZHQz5FLlUlNHdFKWY1JGYoeUwxV0RzMmpUX3MkbzpmXjYnR0dzIkhQIiozejNaYFVjLXVRRHg8XV4yb0A0TyNHY2lUKGZxJ1xHOlBdNik9R20iNCRRITNPUlRHTVkqNCQqKT06UiNcNmMtXTVlYk5VWyVlWmskeSZRKD1jPkBydio9elkoUnRlZXJoRzlYT0hXImY5J0hFKXpaYiQ0KEhWdUI1V2Z0UlRuZClcUmcoKmVFO08nSFAuel9hIypcXHMncE8hZnoubG4heikqKSlbOXM+WyQzbiU+PFtZMShSRCxiIj07dXElKikqXCQpUWYmR1BeY3opKXBMMFEjcGc7XzIqUnpMTGVGMEwmZXkubiUpcGx0VmksNydvTEsjPVFlLyl6LmZcYyRcRDtZNndoRkkqKXpvdiM9RCpwN2R2c1E1Szp3IXpraSxjKSo+JT4mZStZTyV6MkhtMiYqXDssTyI0NnU2OT9sKXlaNyQpZmoiKW9GKmV3bnRHIilSWVxFYV4tNUEuW3AiKT1iXVwtLEFDVSlwJ1FzOjwpMyYpb1YrRSQ9XmNnbXk0KUc1UnNuPVMhRyskXEstLVklZmp4cl42NUhcLEUtbFA0KHlBQiRlT21nKSpwMypwIT0mPnhyUiFSJSpbcTdrNElWLW0/QC0kPjN3dVgsK1U5XCYzKlInXERyS21WJmVtOF0+WV0jeixsXi49bDE0bT5TKDMqPV8ocEg6QFczeV1nbF1lWXkoeSNmQ1kuT3cyPTwhUURucDAxeVooPjpCI3paIikzRGREaE9fVkhBUFUncDJcVmosclQ0dGlgMyF5eD4vPHBQKmZhVWEyQjMmb18oNFVjJz1SW3NiWSpwN0RmJWVrZ2dqZSUqb0orQzRQalI7cloiSCRvI1FKJ2U0SCFlSmQzKkhQViFcelVmSzhITmclSGhSJUdeVkRTJCl6WjsxJ1FiI3A9KGVUZTpRMEVsJCp5PU9BUGgsYXUmejxSJ1IqUWgoM1BOMEwpKkhnQTI7VEtRVCFmRyJvQmJ3ZSo0dENWPl5IMXAnKlshZUwmeXBjIXkoemFxIVwiKlJLJz0rU2EkUUU4WDBdPyxQO1UkeiR5ciFcdEZiZk5GKHpXaiRILjNSNksyI1JNPEpdKz9fJ3AmWygpZT1QTi0/J29mLSJmNG5mJj0jKSlwVnJWJXkoPVs8Mm86aWkvMjtTWlc4cjRabSY9bW00Yj1tYXpfL0wxMmwlUm08Mj5oRFQjKXlIeDBPUXJBeW4pKVFxKiozdFYnKnp4KXojWyg0OkRFQj1XIlEuUmdpIylba3Y5KlJyPilIPk8heVhpJT0oR3ZWQyNIW3d0MSEqZiZSIilSRSYzaCh5JUgpPSVHZV5cJXpfaU5QKyc+X0o9R0smby4hMyZvJ1s+YjpARjwsbFdENXYvMmInXEo3R1dPSTE9XmV3IltzMC1PSiEqKSkpNFhPdkF0ODoiUXBtSFxEWk8tLihIWDA3bTYlZWYrSmsyI1JxR1pbRUJnX0YxTm84OjZfVFAmSCc0cmFGeClSJ2VVPjIoKillWFYsbCVcLkdSeXJoRkx4cSoqPUdNaSllKlxsXSlcQWBpJ1JXKFEnUSl5PF5wJHlfOG1ES0NTST9Yd2B6akxTIWUwVSlwLFNuOylvZ2IlNEkneTgsK0FSME04YT9mJSlHIm8wS2RkeG1hKXp1cidlZSpbXXFvUyhHInonXClIJ2UhNC9mOTV6VydSWXZNY0Q8QCgpSDo+ITMkZnAlSClwZVVDYGM+YlQnPWp5RiFlcy9tMDokKkcpKlxrIlwrZjU+UztEeGkiW21sUUx6RkUkW0VpIzRpRHlkIzQmeUFcRGgsKSp6TFtXSGJQRXFWZGp6Q1RNKilRLXVUQFBPJ1tITlVDPXldVztEVTgnKltPR3NVeC83QDtxakIhUWNwJj1mYSg0azQocCpbJSplJilSdid5X0slPnhtQkBmSTU/bFk3Jj5NcnleRSkpemdEO1olb0E7MmRiLmsncChvKTNEKEh0KnBUZ09dJDR4eCYqPi90L1ImZSxYWkFMST5OLSl5aTA1N3EibzVLTSQ+KVx5U0JAU05dLmQqKW9hckVAYidwUihvNScpKj08L3h1OixeXVBRNSYzczUuODFcTmM5RmZTInlWVSdSb24sMigpKTNwJD0nNF9KRFkwa1YiUTxWJDQ5ajlcPSUqcFZJTi0qNDstITRLaXk+L0ZbaUwtYyhbb1xDak1PVyUpPiVbNSd6I1xkI2UhbzMjKikqXEcjekdVKmVRbidRRjJlTT4mKSkpKWZeLnBUSWYiKT09Jyo0RDYpcD9MaHRyYzxJOmVYPik0RHlHQiE9SiZIL1tZd0JHJG8/JHp3JCk+cVJTaFRvcT5RN0k8Slc0RE8/THopW0gpUiNSNCNlNWxrXClScClHRD1MIW9PPiYqKXAjM0FbXmpkSCMqKlxVOiN5aHRGSnopNEkjKilvakp6KWYhXFhrbyV6JypwKlxheXFucGBwMERXeSpRXzc2c1BZZCczXl5EIT5vJEdwVCxKNHMocHBJcy9aUFdGIjQoRyQ0Mj84cnQxd0hnbCNRJFwvXzIrJGUlUUo4RTEnUT13LTxicD8qXHV4IVJ2NVBDV1hCdWA9VHglbywhW0UjM28xWWhaQzR2OyUpWyQqXCIqM2FAcUl6PU1RZDYhPjVEJj5gMikpSFFCajJcVnppR0I4UTJqJmZnX0hNLiFIZFYhSG1mOHUiPSMqZkkrSz5SbXVVRms7RCZ5QFFyWGZaTk5JbTJDeGlucCdcZGYqKnAkNFpzdihcaUVOcnVHZ2BCWCFmJUc9Rz1GISUnKlw=

_________________________________________________________________________________Exercise 2.5 Digits := 40;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdEaWdpdHNHRigiI1M3I0Yu

x := exp(Pi*sqrt(163));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJ4R0YoLUkkZXhwR0YlNiMqJkkjUGlHRiYiIiIiJGoiI0YzIiIjNyNGLg==

y := evalf(x);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJ5R0YoJCJJV2ZzK0QqKioqKioqKioqKlJ1bzJrN3VgaSMhI0E3I0Yu

printf("%20.20f\134n\134n",y);

262537412640768743.99999999999925007259

z := round(y);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJ6R0YoIjNXKG8yazd1YGkjNyNGLg==

y-z;

JCErY1NGKlwoISNB

restart; _________________________________________________________________________________Exercise 3.1 A := (x^2-4*y^2)*(x^3-x*y^2);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJBR0YoKiYsJiokSSJ4R0YoIiIjIiIiKiRJInlHRihGMiEiJUYzLCYqJEYxIiIkRjMqJkYxRjNGNUYyISIiRjM3I0Yu

simplify(A);

LCgqJEkieEc2IiIiJiIiIiomRiQiIiRJInlHRiUiIiMhIiYqJkYkRidGKiIiJUYu

expand(A);

LCgqJEkieEc2IiIiJiIiIiomRiQiIiRJInlHRiUiIiMhIiYqJkYkRidGKiIiJUYu

factor(A);

KiwsJkkieEc2IiIiIkkieUdGJSEiI0YmLCZGJEYmRiciIiNGJkYkRiYsJkYkRiZGJyEiIkYmLCZGJEYmRidGJkYm

convert(expand(A),horner,x);

KiYsJiokSSJ5RzYiIiIlRicqJiwmKiRJInhHRiYiIiMiIiIqJEYlRiwhIiZGLUYrRixGLUYtRitGLQ==

I would vote for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiwtSShtZmVuY2VkR0YkNiQtRiM2Jy1GLDYlUSJ4RidGL0YyLUkjbW9HRiQ2LVEoJm1pbnVzO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRy8lKXN0cmV0Y2h5R0ZHLyUqc3ltbWV0cmljR0ZHLyUobGFyZ2VvcEdGRy8lLm1vdmFibGVsaW1pdHNHRkcvJSdhY2NlbnRHRkcvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZWLUYjNiYtSSNtbkdGJDYkUSIyRidGQy1GQDYtUTEmSW52aXNpYmxlVGltZXM7RidGQ0ZFRkhGSkZMRk5GUEZSL0ZVUSYwLjBlbUYnL0ZYRl1vLUYsNiVRInlGJ0YvRjJGQ0YrRkNGQ0Zpbi1GODYkLUYjNidGPC1GQDYtUSIrRidGQ0ZFRkhGSkZMRk5GUEZSRlRGV0ZZRitGQ0ZDRmluRjxGaW4tRjg2JC1GIzYmRjxGP0Zfb0ZDRkNGaW4tRjg2JC1GIzYmRjxGZm9GX29GQ0ZDRkNGK0ZD as the most useful version, but of course it depends what you want to use it for._________________________________________________________________________________Exercise 3.2 simplify(2*x/(x^2-1)+1/(x+x^2)+1/(x-x^2));

LCQqJEkieEc2IiEiIiIiIw==

To do this by hand, note that 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 and 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 and 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. Thus, our expression is 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, which simplifies to 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. The numerator here factors as LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNigtSSNtbkdGJDYkUSIyRicvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjsvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkMvJSlzdHJldGNoeUdGQy8lKnN5bW1ldHJpY0dGQy8lKGxhcmdlb3BHRkMvJS5tb3ZhYmxlbGltaXRzR0ZDLyUnYWNjZW50R0ZDLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUi1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRInhGJ0YvRjItRj42LVEiK0YnRjtGQUZERkZGSEZKRkxGTi9GUVEsMC4yMjIyMjIyZW1GJy9GVEZbby1GODYkUSIxRidGO0Y7RjtGPS1GVjYkLUYjNiZGWi1GPjYtUSgmbWludXM7RidGO0ZBRkRGRkZIRkpGTEZORmpuRlxvRl1vRjtGO0Y7RitGOw== and so everything cancels to leave LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1GIzYkLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y0LUYjNiQtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjVRJ2l0YWxpY0YnRjQvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkcvJSliZXZlbGxlZEdRJmZhbHNlRidGNA==. _________________________________________________________________________________Exercise 4.1 plot(sin(x),x=-5..5);

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plot([sin(x),x-x^3/6+x^5/120-x^7/5040],x=-5..5);

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#;7$$"0%ze<+ZWO!#9$!19G&*p'fzf(!#;7$$"1h@V'QAcp$!#:$!1c/,XY!3S)!#;7$$"2XoOtOTEu$!#;$!1JMOj+Yi"*!#;7$$"1h>Ry?w#z$!#:$!2&RQEF;=+5!#;7$$"2ZoOtE,D%Q!#;$!2[pEl[fl3"!#;7$$"1oMpQnq&*Q!#:$!2#4f!>o8F="!#;7$$"1d:Ji#eE%R!#:$!2#HIsje7r7!#;7$$"2xMpQdIo*R!#;$!2<QBj0FxP"!#;7$$"19Fa3prXS!#:$!2#RtF\qey9!#;7$$"1OqS"Q(3%4%!#:$!2$Rvw[g=$e"!#;7$$"1uW*)y65YT!#:$!2jbN?([`,<!#;7$$"2Nd9HQD$)>%!#;$!2jBTN$36F=!#;7$$"1(RzenTeC%!#:$!2YBT9qIy%>!#;7$$"14<Mo=I'H%!#:$!11alKCV$3#!#:7$$"16@U%3YbM%!#:$!1`;n')3"QA#!#:7$$"1b3<Mt#*)R%!#:$!2Lf9+rCeQ#!#;7$$"0#Rycp6XW!#9$!1)pl?_M]`#!#:7$$"0%ze<u;)\%!#9$!2d\!faWp<F!#;7$$"1%\)pRw.[X!#:$!2%3=NwrQ,H!#;7$$"1[#\)phU(f%!#:$!2t<)yw7x&4$!#;7$$"1CZ%*))R&ok%!#:$!2/(*zxy!z.L!#;7$$"1#RycBnsp%!#:$!1z6$f5>5`$!#:7$$"1<LmKWq]Z!#:$!2(ycuzY*)*y$!#;7$$"1Rxa46q*z%!#:$!1XfD`r!\/%!#:7$$"1Gb5@r1[[!#:$!2&e#*pNz_9V!#;7$$"1)Gd9fp(**[!#:$!1c]r5#RRi%!#:7$$"1^-05&f8&\!#:$!1x8zGq?c\!#:7$$"#]!""$!1G(e,teEH&!#:-%&COLORG6'%$RGBG$""!!""$"('>!\&!")$")C)eq%!")-%+_ATTRIBUTEG6#/%'sourceG%,mathdefaultG-%%VIEWG6$;$!#]!""$"#]!""%(DEFAULTG-&%&_AXISG6#"""6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%+AXESLABELSG6$-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"x6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"Q!6"-%)_VISIBLEG6#"""-%%ROOTG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YG6#$""!!""-%-BOUNDS_WIDTHG6#$"%+]!""-%.BOUNDS_HEIGHTG6#$"%+]!""-%)CHILDRENG6"-%+ANNOTATIONG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YG6#$""!!""-%-BOUNDS_WIDTHG6#$"%+]!""-%.BOUNDS_HEIGHTG6#$"%+]!""-%)CHILDRENG6"Ig==

The two graphs are very close together for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= between about LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtb0dGJDYtUSomdW1pbnVzMDtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTi1JI21uR0YkNiRRIjNGJ0Y7RjtGK0Y7 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JFEiM0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yv, but outside that range they move apart very rapidly._________________________________________________________________________________Exercise 5.1 solve({x^2+y^2=1,(x-1)^2+(y-1)^2=1},{x,y});

NiQ8JC9JInhHNiIiIiIvSSJ5R0YmIiIhPCQvRiVGKi9GKUYn

To obtain this by hand, expand out the second equation to get 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, or equivalently 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. Subtracting the first equation gives 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, so 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. Squaring this gives LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNidGKy1GIzYqRistRiM2JC1JJW1zdXBHRiQ2JS1GLDYlUSJ4RidGL0YyLUkjbW5HRiQ2JFEiMkYnL0YzUSdub3JtYWxGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGRS1JI21vR0YkNi1RIitGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZQLyUpc3RyZXRjaHlHRlAvJSpzeW1tZXRyaWNHRlAvJShsYXJnZW9wR0ZQLyUubW92YWJsZWxpbWl0c0dGUC8lJ2FjY2VudEdGUC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRmluLUYjNiQtRjw2JS1GLDYlUSJ5RidGL0YyRkFGR0ZFRkotRiM2KEZBLUZLNi1RMSZJbnZpc2libGVUaW1lcztGJ0ZFRk5GUUZTRlVGV0ZZRmVuL0ZoblEmMC4wZW1GJy9GW29GaW9GPkZlb0Zgb0ZFRitGRS1GSzYtUSI9RidGRUZORlFGU0ZVRldGWUZlbi9GaG5RLDAuMjc3Nzc3OGVtRicvRltvRl9wLUZCNiRRIjFGJ0ZFRkVGK0ZF, and subtracting the first equation gives 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. This means that either LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= or LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= must be zero, and the equation LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNidGKy1GIzYmLUYsNiVRInhGJ0YvRjItSSNtb0dGJDYtUSIrRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlMtRiw2JVEieUYnRi9GMkZALUY9Ni1RIj1GJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjc3Nzc3OGVtRicvRlVGZ24tSSNtbkdGJDYkUSIxRidGQEZARitGQA== means that the other one must be LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yv.Geometrically, the equation 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 describes the circle of radius one centred at the origin, and the equation 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 describes the circle of radius one centred at (1,1). The two circles intersect at the points (1,0) and (0,1), which give the two solutions to our equations. plots[display]( plot([cos(t),sin(t),t=0..2*Pi],color=blue), plot([1+cos(t),1+sin(t),t=0..2*Pi],color=red) );

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_________________________________________________________________________________Exercise 6.1 diff(ln(ln(ln(x))),x);

KihJInhHNiIhIiItSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiNGJS1GJzYjRiZGJQ==

(3*x+4)/(2*x+3);

KiYsJkkieEc2IiIiJCIiJSIiIkYoLCZGJCIiI0YmRighIiI=

diff(%,x);

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simplify(%);

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(1+x^2+x^4/2)*exp(-x^2);

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diff(%,x);

LCYqJiwmKiRJInhHNiIiIiQiIiNGJkYpIiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YnNiMsJCokRiZGKSEiIkYqRioqKCwoRipGKkYyRioqJEYmIiIlI0YqRilGKkYmRipGK0YqISIj

simplify(%);

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_________________________________________________________________________________Exercise 6.2 int(sqrt(1-x^2),x=0..1);

LCRJI1BpRyUqcHJvdGVjdGVkRyMiIiIiIiU=