{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":50499,"title":"Find the area between curves (P2)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none 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transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 32.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 16.25px; text-align: left; transform-origin: 384px 16.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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src=\"data:image/png;base64,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\" 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src=\"data:image/png;base64,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\" width=\"29.5\" height=\"19\" style=\"width: 29.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"76.5\" height=\"18\" style=\"width: 76.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, n)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [0.5, 0.6667, 1.3606, 2.7754, 22.3242]\r\n    assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\n\r\n%%\r\na = 1; \r\nn = 3;\r\n\r\ny_correct = 0.5;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 1; \r\nn = 5; \r\n\r\ny_correct = 0.6667;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2; \r\nn = 2.5; \r\n\r\ny_correct = 1.3606;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nn = 3.1;\r\n\r\ny_correct = 2.7754;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = exp(3);\r\nn = 12;\r\n\r\ny_correct = 22.3242;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T15:56:21.000Z","updated_at":"2025-08-25T11:22:08.000Z","published_at":"2021-02-19T15:59:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Area between curves - Problem 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Find the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = ax^{\\\\frac{1}{n}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e for different \\\"n\\\"  and \\\"a\\\" coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                       Plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and  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the area between curves (P2)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 612.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 306.25px; transform-origin: 407px 306.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Area between curves - Problem 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 32.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 16.25px; text-align: left; transform-origin: 384px 16.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Find the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEEAAAAmCAYAAACbBvanAAAE3UlEQVRoQ+2ZB4hkRRCGvzOLmBWzIp4oimJWzCgGEAVFzDnnHBGzYk6YD8WEGFAwoaJiwoyKiGIEc8KEqJjTt1bLeNdvXve8gTuOaVh22Omurvqruuqv2nGMFuNGGDACwSAYRcIIhH+TweSOBO9fHfgE+GgI+WkRYCHgeeCvUnmTE4TpgH2Bb4Bba5TuY9w0wA7A9MBNwO8lQAwDBGUsAawHzAO8BjwO/NhHAQE4FPh0iACk69RnO2CmUiC6gjAzcCSwFnA4sDhwP3ABcALwSwMQKrk2cGwLWCWOzO1RrzOB+4BH24R0AWFa4IgwXqOejM8XAncAewHfZRRYErgIOBp4o03BDt8vBZwDHAa8309OFxBWCWMfAw4Kj84FbAE8C7yVuVjgTgZ+As4F/uhgZNtRbTM65wBO7XfXoCAkY04EdgJubtMovl8WmADsD7xaeKbLtuWBK4F9gNebBA0Kgm//FkDPb11hkJ5ZETgQ+L6LdYVnZwUuB16JJ5gtm4OCsBVwJ/AgsDPwVYFSswPXAC8DZxXsH9aW44GV+uSogcjSDMDZ8d6uiOrwc4HGhqYJ8yjgnoL9w9pijjoD2AZ4Mye0NBIsOWZ0yU3TagNkI+AGYHPgpQILZwFWBbYENgHmBXYD7o2zhroVxqf1MHAw8GVG7spxZtfYN8mWUhB6D64BPASoxMZNgjPK7BIldduGyjHxkYXjD78B58WzkwVq9J/xpHSOtFvWqfwPM/daKm8DLN03domE3rNepkf1pvzg3QKvusVKsgGwYzDFwmNj24zAq+JOc5DR9HEk57YeYXyw0ruB04cBgqVRQSabfoQod5cgyCwF4esaBIAU0gsAV0ciPqWwN5g7SvjTwwIhZXjLogTEnzZPJHu7gLBgGLI+IDkzGuw8S9bQQUihpWd8Cr610tXlOdgM2Y8cEAn6OODXwotTTlDXbGmuTYzrAk8A71SSJPWtTYy9NqqnlcBeoIabKCOBYHLNMttaEFKCeiT69lxJanJQbYnslZP6lMUGcIB56Klo9W3yJlk1IAxKktKlySMnVZKl+YBLohTvAaxZ2a9Yko2ixkpWA8KcMaTYDNgvsnThsxzblnj829HrlyRUhy/HRCtsiTMvGI2+bXOMfGGd4B1fZJRJ1cyqkjrdTpGwNHA7sFy/0GpBZU9AEP39bUNkzhZtr5Op7QHJmcMX2+/0HFNesCuVsJ3WMMBx0iXBspxf26RbTST4pmWKz0Q++KAmDGKv3ed14d0XMudXAO6K7tSIkQHadicvrxbf61kj44foXXJRoPgNI2Kk242DlRoQbIOlnpIVP+uZ2uV9hwBOhXPjN9+/IW/T4/DV/PF5zyXSZIcyVhqjwc9NU+oZY3DjzNPutfH5lYLQ20DVDFFyIKVEdz7wYi2KFfst5/KKpsbqP1GlICTGJhi+0/cqlMlttWzZCDlxrimzpddWAV0Kgko/AFzcNq8r1NJ7NwWWAS7rM5UuFPe/bTrK4ar/gJFit1ahHAgSkusjQ+8OfBaGm2Tk7LLFYSzvdk7gsOXSAXPMxHoIgOFv0pXZtgKggBwIqWMzMxv6iwZZMXQVPOw1fwCQG8/X3mVJNCGWNldj8nMgSFCs43sDzwFOeGRsDiunylWaE6ZK45NRIxCmgH/NTxERNoqEf9zwNyXzCTaE4DDAAAAAAElFTkSuQmCC\" 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src=\"data:image/png;base64,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\" width=\"29.5\" height=\"19\" style=\"width: 29.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"76.5\" height=\"18\" style=\"width: 76.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, n)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [0.5, 0.6667, 1.3606, 2.7754, 22.3242]\r\n    assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\n\r\n%%\r\na = 1; \r\nn = 3;\r\n\r\ny_correct = 0.5;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 1; \r\nn = 5; \r\n\r\ny_correct = 0.6667;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2; \r\nn = 2.5; \r\n\r\ny_correct = 1.3606;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nn = 3.1;\r\n\r\ny_correct = 2.7754;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = exp(3);\r\nn = 12;\r\n\r\ny_correct = 22.3242;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T15:56:21.000Z","updated_at":"2025-08-25T11:22:08.000Z","published_at":"2021-02-19T15:59:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Area between curves - Problem 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Find the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = ax^{\\\\frac{1}{n}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e for different \\\"n\\\"  and \\\"a\\\" coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                       Plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and  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