Решение. Находим первую производную:
![](data:image/png;base64,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)
.
Из уравнений
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
получаем точки, «подозрительные» на экстремум:
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
. Исследуем их, определяя знак первой производной слева и справа от каждой точки. Для наглядности результаты представим в виде таблицы изменения знака
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAVCAYAAACg/AXsAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEjSURBVDjLzZQxTgJBFIZ/lpYLQJjt7IHRG5jxEbDEBCdTmWxBzDSYbGHMzHbb2Gul9R5B9iIaOQCHMLqLGUNQRxYKKaaY5L0v7/3/P4MkSbDrwb9A3oEaMKrvBLkU7Argr8qY5laQNI0a1EYOLh+3nuQTUsu5sgMvJAMCAHUgC76KljpkgTGqeRjSfZSmDS/knOOhaHpDm3JXbBUfgNFMm/EBkR5t5I6VfFiIN3filWsILm7WJ/BCjKYuA3smbbrlPY5V66cJ/JBidw7MubTDUg8txNmqpdUgY3N6PTnuHZG+qJxYlwdGdFu4cfebFn9DGGZA78W3xjeIy4LLipSyX/kBLh1hJ1kUR60+w9N6KjeC2Cl1QmABhAua2s7+/yf7DfkAPzgDKfCPNukAAAAASUVORK5CYII=)
:
В первой строке указаны интервалы, на которые область определения функции разбивается точками
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAXCAYAAAAC9s/ZAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADzSURBVDjLY2hsbGSgBDOMGjDsDAACRiBmhmJGVLFVTAQNaIg19gYq/sPIIPvaJava6D9Qc32ksS9IjEHWfVdaRwcPUV7I85AtYjCKWJTjJlvMYBw1n+QwqM/zMJRlYHgt65ZTTFYglpen8XrIMOwxjqz3hYmtYmBgYmAIZSZoACjQ8tyMU0xMZJcDnb8QbqAsw25GBuM7sfX1klgN+A8NbVCgyXpkFYG9Ieu+MjQtjR9koEdeno27nPEsnAZkgQIOFNrQQOvoSONxl2XYBRIDGQjm4zOAEB54A8rTQvlc5Yxnh5aXS5NlQJQxw3xsKXIYZGcAkp8OHWijM2gAAAAASUVORK5CYII=)
,
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
и сами эти точки. Во второй строке указаны знаки производной
![](data:image/png;base64,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)
в интервалах монотонности. В третьей строке приведено заключение о поведении функции.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAABAQAAAADoIIM7AAAABGdBTUEAALGOfPtRkwAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAALSURBVBjTY2AAAgAABQABRTthKgAAAABJRU5ErkJggg==)
Исследуемая функция, как следует из таблицы, имеет минимум в точке
![](data:image/png;base64,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)
:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEwAAAApCAYAAACfrs/CAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAOuSURBVGje7ZjNTttAEMcn4Urba/nYPAPJ0mOrHpDZCMItlRwrp0oWQsgHAvIBBZtbpMKd9kI5tcobAOm98AJVCzwA6ivw0V07C5vFduzEQMEbaaRsNorj385//J+Bzc1NUBE/FAQFTAFLLaoAI3AbOXHvmq6hdz/we5mBZdvVCQxwQgFcUDKXRb25IMJY1tAqXV/3BvpLLKeYOWC2bb4ghenPdccZY+slglYotCusOxW2dpz6GIcpxCUgcmi2WqOZA+bWyVvScKf4utUyR8kkdADX9rx9XZ/iMHk4Oq4gYq2oot+NGoY9wMbX8H20Lcsxs8D8DMt1cN2dC5ZwfRwXZr/IcswssPWlmRJC5e9BQKLkmElgzD4YGG2JNS2uHDMHjNkIah8aXIrge69cXDlmChgD09SLC0hbXOOmlEoTE915F1eOqQCjr3wabjvp7ySVIYN115jiU9lORMlxKGDsZn33jPfliyZx27fGEe9XbXtClkgawYyqZEr9wLXdnuyi/2O6oO2EyXEoYCx16QmdxIXFofDvW95N4DO+dhtkqgCFXzNL6/jZNd+On1kHcWF5QCzrtXhyPkB0JD6tGDQE+KhqOxNPBlib1hK/vrTzovzENXPJUYUxjpw9L4Rrn+Q9L/O6LcuTAEZh7HqN5yTp8Ixw63iON6LssVsCdBxVGPsVYPZ0Qmi2XTXNl3ey1yJFBKXjum2Phx9mWLTzjyJJ18DzYn1hrYSGtSYDJu8lvRFegFnRByidyWC6k4MzbLjzIYd5ERpSEX8wYP4po988i1hWEWJVu3OjhgxskBvhIxakLTeCgMmfDyj9kTSiPzDhlFm9sTTtAwcUBGzwBhg6SYAllWTkISaI+MB0p8KK8xtifbydLdF6lgIwdhA1nN+TJwY31w6YJPy3krw5fUK2pwtkR7YDrOhTv1RKCkjMBr/wl7/JJtF7erKiP+SBPDwwBIe0KP8J+uPspKlkVpO4cj8zhWxAswdBjtqbrT9ApgwNTPRarFYYhlGOdu3oJ3PlabYy9gCG+NGAeU9G6o1M2xwvIzgIm0aKrjzNVob3mf2ue1+TjLgeTgIA5wCF86jhWlR/OHBfmtLvDBreJEMw6qn3ks8pvIEhwKkCFlOKBsYb5TLaUsBijqhYzfTMuAIWQ4rY2LjpXhSw/lLsafcUsPBg3QTRm+9517GooTWY1H5UTfNVP1+ZSWByT+qPmnJX7H0/H5h5W6EkqYDdf3hT4JBhgAKWVvOtQgG7l/gHvRB+9tRBs+gAAAAASUVORK5CYII=)
.
Точки
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC0AAAATCAYAAAAEaoRHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAE/SURBVEjHY2hsbGQYanjIOXjU0dTGqxgYmBgYVjENGUenpYXyuckw7GWQ8diT1tHBM+gdXV8fK2nEwHCLkYHh75BxNAznuMkWE+VoIAB6kIEZihlRxbCnrwF3dEOssTfQgX8YGWRfu2RVG/0HOrg+0tgXJMYg674L2QBIRoF7EAumzJNEOxqG8zxkixiMIhaBNRpHzcemJsqYYT7YM7gwFn2keJRkR9fneRjKMjC8lnXLKaZmlJPiUZIdXV6exushw7DHOLLeF385OkiSByjj5bkZp5iYyC4H+nwhSOw/JDMyUpo8SHR0CUFHQx3GDMp4sh5ZReAkIuu+MjQtjR/kCY/iBgN6lRyhQHdEGDEsYpBx2wuyHz3A4IwsUOZDCqGOjjQed1mGXSAxkCfoXbkgYk3uJXqAjTaYRh093BwNAHpMsrv/nopYAAAAAElFTkSuQmCC)
и
![](data:image/png;base64,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)
не являются точками экстремума, так как в первой точке функция не определена, а в окрестности второй точки первая производная сохраняет знак.
Пример 4. Найти асимптоты графика функции
![](data:image/png;base64,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)
.
Решение. Точка
![](data:image/png;base64,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)
является точкой разрыва функции. Так как
![](data:image/png;base64,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)
,
то прямая
![](data:image/png;base64,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)
служит вертикальной асимптотой
графика функции [см. формулы (7)].
Ищем наклонные асимптоты
![](data:image/png;base64,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)
, используя формулы (6):
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
.
Таким образом, уравнение наклонной асимптоты имеет вид
![](data:image/png;base64,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)
.
Пример 5. Построить график функции
![](data:image/png;base64,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)
, используя общую схему исследования функции.
Решение.
Область определения функции:
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
. Функция не является симметричной и периодической. Находим предельные значения функции:
![](data:image/png;base64,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)
;
![](data:image/png;base64,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)
;
![](data:image/png;base64,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)
.
График функции имеет одну вертикальную асимптоту
![](data:image/png;base64,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)
и одну наклонную асимптоту
![](data:image/png;base64,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)
(см. пример 4). Он пересекает координатные оси в точке
![](data:image/png;base64,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)
.
Функция имеет один минимум при
![](data:image/png;base64,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)
(см пример 3).
Вторая производная
![](data:image/png;base64,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)
обращается в бесконечность при
![](data:image/png;base64,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)
и равна нулю в точке
![](data:image/png;base64,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)
, которая является единственной точкой перегиба (см. таблицу):
Учитывая полученные результаты, строим график функции (рис. 8)
![](data:image/png;base64,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)
:
![](data:image/jpeg;base64,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)
Рисунок 8
Пример 6. Найти первую производную функции y=f(x) , заданной параметрически:
![](data:image/png;base64,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)
.
Решение. Дифференцируем
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
по параметру
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAQCAYAAADESFVDAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACsSURBVCjPY2hsbGQghBnIVgQEjAwM/xlxKgIpqM5yMTb1yEvGqmgVAwMTSIEsg+xNl6xqY5AGDEVRxgzzgfb8A8r9BSr4Yxzb4I3VOqDChbIeeUU4HV5eHitlxCB7yiOv3hCnohw32RIGWY/daR0dPFgVdXSk8XjIMOwBWQXyAFZF9XkehrIMRqdDy7PUPeRMZsbW10tiKGqINfYG+YiBQe6lR3GDAXWihXaKAE1GywUyt7oJAAAAAElFTkSuQmCC)
:
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
. Искомая производная от y по x равна отношению производных от
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
по
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAQCAYAAADESFVDAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACsSURBVCjPY2hsbGQghBnIVgQEjAwM/xlxKgIpqM5yMTb1yEvGqmgVAwMTSIEsg+xNl6xqY5AGDEVRxgzzgfb8A8r9BSr4Yxzb4I3VOqDChbIeeUU4HV5eHitlxCB7yiOv3hCnohw32RIGWY/daR0dPFgVdXSk8XjIMOwBWQXyAFZF9XkehrIMRqdDy7PUPeRMZsbW10tiKGqINfYG+YiBQe6lR3GDAXWihXaKAE1GywUyt7oJAAAAAElFTkSuQmCC)
:
![](data:image/png;base64,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)
.
Пример 7. Найти частные производные
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
функции
![](data:image/png;base64,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)
.
Решение. Считая функцию
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADTSURBVDjLY2hsbGQgFTMMjCYgYARiZgaGVUwwsf9gsf+MWDWBNNRHGvsCVfxlMI5eABPPcZMtlvXIK8KqqSHW2JvBOGo+UFEJTBHIoCgj2T6PvHpDnM4rL4+VMmKQPQVTVJ3lYiTLYHQqtr5eEqcmkPMYZD12p3V08IBtMWZYiOxUrJpAikBOg/lPVlb2iHF0gw/OgKivj5UEOc0lq9oY6CxjOROPme5yxrNDq0ONjY2j6/BoYrgFtOUPg6z7rrw8Dxs5BoaXDAxGt/D6aZAnI2IxAJrxEErOAiiLAAAAAElFTkSuQmCC)
функцией только одной переменной
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC+SURBVDjLY2hsbGQgFTMMjCYgYARiZihmRBVbxYRVU0OssTdQwR9GBtnXLlnVRv+BGuojjX1BYgyy7rvSOjp4cDovz0O2iMEoYlGOm2wxg3HUfKL8VJ/nYSjLwPBa1i2nmOiAKC9P4/WQYdhjHFnvS5QmkMfz3IxTTExklwOdthAk9h8SGIwYmqASzCCPy3pkFYGdKOu+MjQtjR9kiEdxgwGGpiyQ50GhBPV4R0caj7sswy6QGMiQQZAiaKoJAHMADRdLWqSBAAAAAElFTkSuQmCC)
, а переменные
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADrSURBVDjL1ZI/DgFBGMUfWhcgZs+A4QayPkFJwmQqyRaKaRRbiMxst41ep98j4CIkDuAQEkZCxN+JiEQxxZt8v+S9732IogifPnwVToA0gAyQpC9DQOpaP4X7HPPj8B4FWgVxnLV/RvImGC3P+qVtI3gL4Fupdc7qOA6yPvcnTrBWVGJga1K6ZHUYyjyR6jgtTGuZ48CWC9OyeZXvd88u3OGebo+HtXKV1MC5KpuRClgxomnFo9lt1vcwwxIobx7ZvYOvu7RdCyEazkdy2jCrJ0EY5BsMCy5N0xk2Iyp6wA7wdjQyxd/f9n/AB8j8bUTpDv6cAAAAAElFTkSuQmCC)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAANCAYAAABy6+R8AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACHSURBVCjPY2hsbGQgFTNQRdMqBgYmBgYGZjTMiFNTR0caj6cswy6goj8gzMjA8I+BQfaVR3GDAU5N9XmRqpF59aowG6ONGRYYxzZ4E+UnfBpw+gmfBgxN6BrQAwBD03+ggggjhkWGkbV+sFCrDg01iq2vl8SpKctDtggWanBsHDWfdpFLM00AT6TmnzvnNkAAAAAASUVORK5CYII=)
рассматривая как постоянные [см. формулу (8)], находим
![](data:image/png;base64,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)
. Аналогично, считая
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADTSURBVDjLY2hsbGQgFTMMjCYgYARiZgaGVUwwsf9gsf+MWDWBNNRHGvsCVfxlMI5eABPPcZMtlvXIK8KqqSHW2JvBOGo+UFEJTBHIoCgj2T6PvHpDnM4rL4+VMmKQPQVTVJ3lYiTLYHQqtr5eEqcmkPMYZD12p3V08IBtMWZYiOxUrJpAikBOg/lPVlb2iHF0gw/OgKivj5UEOc0lq9oY6CxjOROPme5yxrNDq0ONjY2j6/BoYrgFtOUPg6z7rrw8Dxs5BoaXDAxGt/D6aZAnI2IxAJrxEErOAiiLAAAAAElFTkSuQmCC)
функцией только
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADrSURBVDjL1ZI/DgFBGMUfWhcgZs+A4QayPkFJwmQqyRaKaRRbiMxst41ep98j4CIkDuAQEkZCxN+JiEQxxZt8v+S9732IogifPnwVToA0gAyQpC9DQOpaP4X7HPPj8B4FWgVxnLV/RvImGC3P+qVtI3gL4Fupdc7qOA6yPvcnTrBWVGJga1K6ZHUYyjyR6jgtTGuZ48CWC9OyeZXvd88u3OGebo+HtXKV1MC5KpuRClgxomnFo9lt1vcwwxIobx7ZvYOvu7RdCyEazkdy2jCrJ0EY5BsMCy5N0xk2Iyp6wA7wdjQyxd/f9n/AB8j8bUTpDv6cAAAAAElFTkSuQmCC)
, а затем только
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAANCAYAAABy6+R8AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACHSURBVCjPY2hsbGQgFTNQRdMqBgYmBgYGZjTMiFNTR0caj6cswy6goj8gzMjA8I+BQfaVR3GDAU5N9XmRqpF59aowG6ONGRYYxzZ4E+UnfBpw+gmfBgxN6BrQAwBD03+ggggjhkWGkbV+sFCrDg01iq2vl8SpKctDtggWanBsHDWfdpFLM00AT6TmnzvnNkAAAAAASUVORK5CYII=)
, получаем
![](data:image/png;base64,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)
,
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