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{"save":1,"level":1,"time":"90","total":34,"point":5,"segment":[{"id":"3592","test_id":"484","question":"<p>Cho hàm s\u1ed1 <span class=\"math-tex\">$y=f(x) $<\/span> xác \u0111\u1ecbnh trên <span class=\"math-tex\">$\\mathbb R$<\/span> và có b\u1ea3ng bi\u1ebfn thiên nh\u01b0 sau:<\/p><p><span class=\"svgedit\"><svg height=\"160\" width=\"360\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"162\" id=\"canvas_background\" width=\"362\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_9\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <g id=\"svg_39\"> <line fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"1\" x2=\"358.99999\" y1=\"30.65\" y2=\"30.65\"><\/line> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"1\" x2=\"358.99999\" y1=\"61\" y2=\"61\"><\/line> <line fill=\"none\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"44\" x2=\"44\" y1=\"2.65\" y2=\"162.64998\"><\/line> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_4\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"17\" xml:space=\"preserve\" y=\"24.65\">x<\/text> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_5\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"17\" xml:space=\"preserve\" y=\"53.64999\">y'<\/text> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_6\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"17\" xml:space=\"preserve\" y=\"97.64999\">y<\/text> <g id=\"svg_10\"> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_11\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-90 68.00000000000001,17.249999999999996) \" x=\"62\" xml:space=\"preserve\" y=\"25.64999\">8<\/text> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_12\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(1.5003259181976318,0,0,1,-19.51270890111573,0) \" x=\"44.33217\" xml:space=\"preserve\" y=\"22.64999\">-<\/text> <\/g> <g id=\"svg_16\"> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_14\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-90 342.99996948242193,148.25000000000003) \" x=\"336.99997\" xml:space=\"preserve\" y=\"156.64999\">8<\/text> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_15\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(1.5003259181976318,0,0,1,-19.51270890111573,0) \" x=\"227.62566\" xml:space=\"preserve\" y=\"153.64999\">-<\/text> <\/g> <g id=\"svg_19\"> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_17\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-90 344.00000000000006,19.249999999999975) \" x=\"338\" xml:space=\"preserve\" y=\"27.64999\">8<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_18\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"322\" xml:space=\"preserve\" y=\"26.64999\">+<\/text> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_20\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"142\" xml:space=\"preserve\" y=\"22.65\">7<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_21\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"242.99999\" xml:space=\"preserve\" y=\"22.65\">4<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_22\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(1.5003259181976318,0,0,1,-71.04366943032801,0) \" x=\"134\" xml:space=\"preserve\" y=\"21.65\">-<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_23\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(1.5003259181976318,0,0,1,-71.04366943032801,0) \" x=\"201.3187\" xml:space=\"preserve\" y=\"21.65\">-<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_24\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"140\" xml:space=\"preserve\" y=\"53.64999\">0<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_25\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"241.99999\" xml:space=\"preserve\" y=\"53.65\">0<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_26\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(1.5003259181976318,0,0,1,-71.04366943032801,0) \" x=\"113.33782\" xml:space=\"preserve\" y=\"51.65\">-<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_27\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(1.5003259181976318,0,0,1,-71.04366943032801,0) \" x=\"237.31088\" xml:space=\"preserve\" y=\"51.65\">-<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_28\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"189.99999\" xml:space=\"preserve\" y=\"52\">+<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_29\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"142\" xml:space=\"preserve\" y=\"124.64999\">6<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_30\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"243\" xml:space=\"preserve\" y=\"82.64999\">3<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_31\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(1.5003259181976318,0,0,1,-71.04366943032801,0) \" x=\"134\" xml:space=\"preserve\" y=\"123.65\">-<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_32\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(1.5003259181976318,0,0,1,-71.04366943032801,0) \" x=\"201.3187\" xml:space=\"preserve\" y=\"81.65\">-<\/text> <g id=\"svg_13\" stroke=\"null\" transform=\"rotate(41.14218521118164 296.1072692871093,110.6163787841797) \"> <line fill=\"none\" id=\"svg_7\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"247.35792\" x2=\"341.97313\" y1=\"111.63382\" y2=\"111.28381\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_8\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(0.9557092189788817,0,0,1.075757622718811,15.164872253451902,-9.61240345366059) \" x=\"330.95365\" xml:space=\"preserve\" y=\"120.41056\">><\/text> <\/g> <g id=\"svg_35\" stroke=\"null\" transform=\"rotate(37.457794189453125 104.99973297119143,93.25308227539062) \"> <line fill=\"none\" id=\"svg_33\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"76.39577\" x2=\"131.91125\" y1=\"93.99595\" y2=\"93.64594\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_34\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(0.5607624448651762,0,0,1.075757622718811,74.24600693225261,-11.246218861413581) \" x=\"91.83363\" xml:space=\"preserve\" y=\"105.53356\">><\/text> <\/g> <g id=\"svg_38\"> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_36\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-90 69.00000000000001,73.25) \" x=\"63\" xml:space=\"preserve\" y=\"81.64999\">8<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" id=\"svg_37\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"47\" xml:space=\"preserve\" y=\"80.64999\">+<\/text> <\/g> <g id=\"svg_44\" stroke=\"null\" transform=\"rotate(-25.364763259887695 193.92535400390634,96.44869995117189) \"> <line fill=\"none\" id=\"svg_42\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"160.50844\" x2=\"225.36312\" y1=\"96.85905\" y2=\"96.50904\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_43\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(0.6550977378967309,0,0,1.075757622718811,58.57571728952581,-11.246218861413581) \" x=\"243.59926\" xml:space=\"preserve\" y=\"108.19503\">><\/text> <\/g> <\/g> <\/g> <\/svg><\/span><\/p><p>\u0110i\u1ec3m c\u1ef1c \u0111\u1ea1i c\u1ee7a hàm s\u1ed1 <span class=\"math-tex\">$y=f(x) $<\/span> là:<\/p>","options":["A. x = –7","B. x = –6","C. x = –3","D. x = –4"],"correct":"4","answer":"<p>\u0110áp án \u0111úng là: <span style=\"color:#16a085;\"><strong>D. x = –4.<\/strong><\/span><\/p><p>T\u1eeb b\u1ea3ng bi\u1ebfn thiên ta có:<\/p><p>+ Hàm s\u1ed1 \u0111\u1ea1t c\u1ef1c \u0111\u1ea1i t\u1ea1i x = –4 và <span class=\"math-tex\">$y_{_{C\u0110}}=y(-4)=-3$<\/span>.<\/p><p>+ Hàm s\u1ed1 \u0111\u1ea1t c\u1ef1c ti\u1ec3u t\u1ea1i x = –7 và <span class=\"math-tex\">$y_{_{CT}}=y(-7)=-6$<\/span>.<\/p><p>V\u1eady \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i c\u1ee7a hàm s\u1ed1 là x = –4.<\/p>","type":"choose","user_id":"126","test":"3","date":"2025-04-24 16:33:58"},{"id":"3606","test_id":"484","question":"<p>Nguyên hàm F(x) c\u1ee7a hàm s\u1ed1 <span class=\"math-tex\">$f(x)=\\dfrac{1}{x}+e$<\/span> là<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$F(x)=-\\dfrac{1}{x^2} +e^x+C$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$F(x)=\\ln|x| +ex+C$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$F(x)=\\ln|x| +e^x+C$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$F(x)=\\ln x +e+C$<\/span>"],"correct":"2","answer":"<p>\u0110áp án \u0111úng là: <span style=\"color:#16a085;\"><strong>B. <span class=\"math-tex\">$F(x)=\\ln|x| +ex+C$<\/span>.<\/strong><\/span><\/p><p><span class=\"math-tex\">$F(x)=\\displaystyle\\int f(x)dx=\\displaystyle\\int\\bigg(\\dfrac{1}{x}+e\\bigg)dx=\\ln|x|+ex+C$<\/span><\/p>","type":"choose","user_id":"126","test":"1","date":"2025-04-24 17:24:20"}]}