{"common":{"save":0,"post_id":"7095","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5301","post_id":"7095","mon_id":"1158924","chapter_id":"1159163","question":"<p>Gi\u1edbi h\u1ea1n&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to -2}\\dfrac{x+1}{(x+2)^2}$<\/span> b\u1eb1ng:<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$-\\infty$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{3}{16}$<\/span>","<strong>C.<\/strong> 0","<strong>D.<\/strong> <span class=\"math-tex\">$+\\infty$<\/span>"],"correct":"1","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong>&nbsp;<span class=\"math-tex\">$-\\infty$<\/span><\/span><\/p><p><span class=\"math-tex\">$\\lim_\\limits{x\\to -2}\\dfrac{x+1}{(x+2)^2}=\\lim_\\limits{x\\to -2}\\dfrac{1}{(x+2)^2}.(x+1)=-\\infty$<\/span><\/p><p>V&igrave;&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to -2}\\dfrac{1}{(x+2)^2}=+\\infty$<\/span>&nbsp;v&agrave;&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to -2}(x+1)=-1&lt;0$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-03 03:28:00","option_type":"math","len":0},{"id":"5303","post_id":"7095","mon_id":"1158924","chapter_id":"1159163","question":"<p>Cho I =&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to 0}\\dfrac{2(\\sqrt{3x+1}-1)}{x}$<\/span>&nbsp;v&agrave; J =&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to -1}\\dfrac{x^2-x-2}{x+1}$<\/span>. T&iacute;nh I&nbsp;&ndash; J.<\/p>","options":["<strong>A.<\/strong> 0","<strong>B.<\/strong> 3","<strong>C.<\/strong> &ndash;6","<strong>D.<\/strong> 6"],"correct":"4","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>D.<\/strong>&nbsp;6<\/span><\/p><p>I =&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to 0}\\dfrac{2(\\sqrt{3x+1}-1)}{x}$<\/span>&nbsp;=&nbsp;<strong><span class=\"math-tex\">$\\lim_\\limits{x\\to 0}\\dfrac{6x}{x(\\sqrt{3x+1}+1)}$<\/span><\/strong>&nbsp;=&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to 0}\\dfrac{6}{\\sqrt{3x+1}+1}$<\/span>&nbsp;= 3<\/p><p>J =&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to -1}\\dfrac{x^2-x-2}{x+1}$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to -1}\\dfrac{(x+1)(x-2)}{x+1}$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to -1}(x-2)=-3$<\/span><\/p><p>V\u1eady I&nbsp;&ndash; J = 3 + 3 = 6<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-03 03:33:00","option_type":"txt","len":1},{"id":"5304","post_id":"7095","mon_id":"1158924","chapter_id":"1159163","question":"<p>T&igrave;m gi\u1edbi h\u1ea1n <span class=\"math-tex\">$\\lim_\\limits{x\\to 1^+}\\dfrac{4x-3}{x-1}$<\/span>.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$+\\infty$<\/span>","<strong>B.<\/strong> 2","<strong>C.<\/strong> <span class=\"math-tex\">$-\\infty$<\/span>","<strong>D.<\/strong> &ndash;2"],"correct":"1","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong>&nbsp;<span class=\"math-tex\">$+\\infty$<\/span><\/span><\/p><p><span class=\"math-tex\">$\\lim_\\limits{x\\to 1^+}\\dfrac{4x-3}{x-1}$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$+\\infty$<\/span><\/p><p>V&igrave;&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to 1^+}(4x-3)=1>0$<\/span>v&agrave;&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to 1^+}(x-1)=0$<\/span>&nbsp;v&agrave;&nbsp;<span class=\"math-tex\">$x-1>0$<\/span>&nbsp;khi&nbsp;<span class=\"math-tex\">$x\\to1^+$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-03 03:38:03","option_type":"math","len":0}]}