Đường tiệm cận của đồ thị hàm số

Home Lớp 12 Toán lớp 12 - Sách Kết nối tri thức Bài 3. Đường tiệm cận của đồ thị hàm sốBài tập cơ bản

{"common":{"save":0,"post_id":"7520","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5382","post_id":"7520","mon_id":"1159285","chapter_id":"1159288","question":"Cho hàm s\u1ed1 $y=f(x)$<\/span> có $\\displaystyle\\lim_{x\\to+\\infty}f(x)=1$<\/span> và $\\displaystyle\\lim_{x\\to-\\infty}f(x)=-1$<\/span>. Kh\u1eb3ng \u0111\u1ecbnh nào sau \u0111ây là kh\u1eb3ng \u0111\u1ecbnh \u0111úng?<\/p>","options":["A.<\/strong> \u0110\u1ed3 th\u1ecb hàm s\u1ed1 \u0111ã cho có hai ti\u1ec7m c\u1eadn ngang là các \u0111\u01b0\u1eddng th\u1eb3ng x = 1 và x = –1.","B.<\/strong> \u0110\u1ed3 th\u1ecb hàm s\u1ed1 \u0111ã cho không có ti\u1ec7m c\u1eadn ngang.","C.<\/strong> \u0110\u1ed3 th\u1ecb hàm s\u1ed1 \u0111ã cho có \u0111úng m\u1ed9t ti\u1ec7m c\u1eadn ngang.","D.<\/strong> \u0110\u1ed3 th\u1ecb hàm s\u1ed1 \u0111ã cho có hai ti\u1ec7m c\u1eadn ngang là các \u0111\u01b0\u1eddng th\u1eb3ng y = 1 và y = –1."],"correct":"4","level":"1","hint":"S\u1eed d\u1ee5ng \u0111\u1ecbnh ngh\u0129a \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang.<\/p>\u0110\u01b0\u1eddng th\u1eb3ng $y=y_0$<\/span> là \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang (hay ti\u1ec7m c\u1eadn ngang) c\u1ee7a \u0111\u1ed3 th\u1ecb hàm s\u1ed1 y = f(x) n\u1ebfu ít nh\u1ea5t m\u1ed9t trong các \u0111i\u1ec1u ki\u1ec7n sau \u0111\u01b0\u1ee3c th\u1ecfa mãn $\\displaystyle\\lim_{x\\to+\\infty}f(x)=y_0$<\/span>, $\\displaystyle\\lim_{x\\to-\\infty}f(x)=y_0$<\/span>.<\/p>","answer":"Ch\u1ecdn D.<\/strong> \u0110\u1ed3 th\u1ecb hàm s\u1ed1 \u0111ã cho có hai ti\u1ec7m c\u1eadn ngang là các \u0111\u01b0\u1eddng th\u1eb3ng y = 1 và y = –1<\/span>.<\/p>D\u1ef1a vào \u0111\u1ecbnh ngh\u0129a \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb hàm s\u1ed1 ta ch\u1ecdn \u0111áp án D<\/strong>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-06-29 01:29:02","option_type":"txt","len":3},{"id":"5383","post_id":"7520","mon_id":"1159285","chapter_id":"1159288","question":"Cho hàm s\u1ed1 f(x) có b\u1ea3ng bi\u1ebfn thiên nh\u01b0 sau.<\/p><svg height=\"140\" width=\"320\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g><title><\/title><rect fill=\"#fff\" height=\"142\" id=\"canvas_background\" width=\"322\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><image height=\"142\" id=\"svg_1\" stroke=\"null\" width=\"321.99999\" x=\"-1.5\" 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\" y=\"0.5\"><\/image> <\/g> <\/svg><\/span><\/p>T\u1ed5ng s\u1ed1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng và ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb hàm s\u1ed1 \u0111ã cho là<\/p>","options":["A.<\/strong> 1","B.<\/strong> 2","C.<\/strong> 4","D.<\/strong> 3"],"correct":"2","level":"1","hint":"S\u1eed d\u1ee5ng \u0111\u1ecbnh ngh\u0129a \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang, \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn \u0111\u1ee9ng.<\/p>","answer":"Ch\u1ecdn B.<\/strong> 2.<\/span><\/p>T\u1eeb b\u1ea3ng bi\u1ebfn thiên \u0111ã cho ta có<\/p>$\\displaystyle\\lim_{x\\to-\\infty}f(x)=0$<\/span> nên \u0111\u01b0\u1eddng th\u1eb3ng y = 0 là m\u1ed9t ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb hàm s\u1ed1.<\/p>$\\displaystyle\\lim_{x\\to0}f(x)=-\\infty$<\/span> nên \u0111\u01b0\u1eddng th\u1eb3ng x = 0 là m\u1ed9t ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb hàm s\u1ed1.<\/p>V\u1eady \u0111\u1ed3 th\u1ecb hàm s\u1ed1 \u0111ã cho có 2 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-06-29 01:43:23","option_type":"txt","len":0},{"id":"5384","post_id":"7520","mon_id":"1159285","chapter_id":"1159288","question":"Cho hàm s\u1ed1 có b\u1ea3ng bi\u1ebfn thiên nh\u01b0 hình sau.<\/p><svg height=\"170\" width=\"320\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g><title><\/title><rect fill=\"#fff\" height=\"172\" id=\"canvas_background\" width=\"322\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><image height=\"164\" id=\"svg_1\" stroke=\"null\" width=\"320\" x=\"0.5\" 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\" y=\"0.5\"><\/image> <\/g> <\/svg><\/span><\/p>T\u1ed5ng s\u1ed1 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang và ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb hàm s\u1ed1 y = f(x) là<\/p>","options":["A.<\/strong> 3","B.<\/strong> 1","C.<\/strong> 2","D.<\/strong> 4"],"correct":"4","level":"1","hint":"S\u1eed d\u1ee5ng \u0111\u1ecbnh ngh\u0129a \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn \u0111\u1ee9ng, \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang.<\/p>","answer":"Ch\u1ecdn D.<\/strong> 4.<\/span><\/p>$\\displaystyle\\lim_{x\\to-\\infty}y=4$<\/span>, $\\displaystyle\\lim_{x\\to+\\infty}y=-1$<\/span> ⇒ \u0110\u1ed3 th\u1ecb hàm s\u1ed1 có hai ti\u1ec7m c\u1eadn ngang là y = 4 và y = –1.<\/p>$\\displaystyle\\lim_{x\\to-1^-}y=+\\infty$<\/span>, $\\displaystyle\\lim_{x\\to-1^+}y=-\\infty$<\/span> ⇒ \u0110\u1ed3 th\u1ecb hàm s\u1ed1 có ti\u1ec7m c\u1eadn \u0111\u1ee9ng là x = –1.<\/p>$\\displaystyle\\lim_{x\\to1^-}y=-\\infty$<\/span>, $\\displaystyle\\lim_{x\\to1^+}y=-\\infty$<\/span> ⇒ \u0110\u1ed3 th\u1ecb hàm s\u1ed1 có ti\u1ec7m c\u1eadn \u0111\u1ee9ng là x = 1.<\/p>V\u1eady \u0111\u1ed3 th\u1ecb hàm s\u1ed1 có 4 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-06-29 02:09:09","option_type":"txt","len":0}]}