{"common":{"save":0,"post_id":"7089","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5250","post_id":"7089","mon_id":"1158924","chapter_id":"1159163","question":"<p>Gi&aacute; tr\u1ecb c\u1ee7a gi\u1edbi h\u1ea1n&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to -\\infty}\\dfrac{2x^3-7x^2+11}{3x^6+2x^5-5}$<\/span> l&agrave;:<\/p>","options":["<strong>A.<\/strong> &ndash;2","<strong>B.<\/strong> <span class=\"math-tex\">$+\\infty$<\/span>","<strong>C.<\/strong> 0","<strong>D.<\/strong> <span class=\"math-tex\">$-\\infty$<\/span>"],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong>&nbsp;0<\/span><\/p><p><span class=\"math-tex\">$\\lim_\\limits{x\\to -\\infty}\\dfrac{2x^3-7x^2+11}{3x^6+2x^5-5}$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to -\\infty}\\dfrac{\\dfrac{2}{x^3}-\\dfrac{7}{x^4}+\\dfrac{11}{x^6}}{3+\\dfrac{2}{x}-\\dfrac{5}{x^6}}$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$\\dfrac{0}{3}=0$<\/span><\/p>","type":"choose","extra_type":"shape2","user_id":"131","test":"0","date":"2024-02-29 01:55:52","option_type":"math","len":0},{"id":"5252","post_id":"7089","mon_id":"1158924","chapter_id":"1159163","question":"<p>Gi&aacute; tr\u1ecb c\u1ee7a gi\u1edbi h\u1ea1n&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to -\\infty}\\dfrac{2x-3}{\\sqrt{x^2+1}-x}$<\/span> l&agrave;:<\/p>","options":["<strong>A.<\/strong> &ndash;2","<strong>B.<\/strong> <span class=\"math-tex\">$+\\infty$<\/span>","<strong>C.<\/strong> 3","<strong>D.<\/strong> &ndash;1"],"correct":"4","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>D.<\/strong>&nbsp;&ndash;1<\/span><\/p><p>Khi <span class=\"math-tex\">$x\\to -\\infty$<\/span>&nbsp;th&igrave;&nbsp;<span class=\"math-tex\">$\\sqrt{x^2}=|x|=-x$<\/span>. Suy ra&nbsp;<span class=\"math-tex\">$\\sqrt{x^2+1}-x:\\sqrt{x^2}-x=-x-x=-2x\\ne0$<\/span><\/p><p>Do \u0111&oacute; chia c\u1ea3 t\u1eed v&agrave; m\u1eabu cho x ta \u0111\u01b0\u1ee3c<\/p><p><span class=\"math-tex\">$\\lim_\\limits{x\\to -\\infty}\\dfrac{2x-3}{\\sqrt{x^2+1}-x}$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to -\\infty}\\dfrac{2-\\dfrac{3}{x}}{-\\sqrt{1+\\dfrac{1}{x^2}}-1}$<\/span>&nbsp;=&nbsp;&ndash;1<\/p>","type":"choose","extra_type":"sheep","user_id":"131","test":"0","date":"2024-02-29 02:09:58","option_type":"math","len":0},{"id":"5254","post_id":"7089","mon_id":"1158924","chapter_id":"1159163","question":"<p>Bi\u1ebft r\u1eb1ng&nbsp;<span class=\"math-tex\">$\\dfrac{(2-a)x-3}{\\sqrt{x^2+1}-x}$<\/span> c&oacute; gi\u1edbi h\u1ea1n l&agrave;&nbsp;<span class=\"math-tex\">$+\\infty$<\/span> khi&nbsp;<span class=\"math-tex\">$x\\to +\\infty$<\/span> (v\u1edbi a l&agrave; tham s\u1ed1). T&iacute;nh gi&aacute; tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a P = a&sup2;&nbsp;&ndash; 2a + 4.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$P_{min}=1$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$P_{min}=3$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$P_{min}=4$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$P_{min}=5$<\/span>"],"correct":"2","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong>&nbsp;<span class=\"math-tex\">$P_{min}=3$<\/span><\/span><\/p><p>Khi <span class=\"math-tex\">$x\\to +\\infty$<\/span>&nbsp;th&igrave;&nbsp;<span class=\"math-tex\">$\\sqrt{x^2}=|x|=x$<\/span>. Suy ra&nbsp;<span class=\"math-tex\">$\\sqrt{x^2+1}-x:\\sqrt{x^2}-x=x-x=0$<\/span><\/p><p>Do \u0111&oacute; nh&acirc;n l\u01b0\u1ee3ng li&ecirc;n h\u1ee3p&nbsp;ta \u0111\u01b0\u1ee3c<\/p><p><span class=\"math-tex\">$\\lim_\\limits{x\\to +\\infty}\\dfrac{(2-a)x-3}{\\sqrt{x^2+1}-x}$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to +\\infty}[(2-a)x-3](\\sqrt{x^2+1}+x)$<\/span><\/p><p>=&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to +\\infty}x^2\\bigg(2-a-\\dfrac{3}{x}\\bigg)\\bigg(\\sqrt{1+\\dfrac{1}{x^2}}+1\\bigg)$<\/span><\/p><p>V&igrave;&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to +\\infty}x^2=+\\infty$<\/span>&nbsp;v&agrave;&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to +\\infty}\\bigg(\\sqrt{1+\\dfrac{1}{x^2}}+1\\bigg)=2>0$<\/span>&nbsp;m&agrave;&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to +\\infty}\\dfrac{(2-a)x-3}{\\sqrt{x^2+1}-x}=+\\infty$<\/span><\/p><p>n&ecirc;n&nbsp;<span class=\"math-tex\">$\\lim_\\limits{x\\to +\\infty}\\bigg(2-a-\\dfrac{3}{x}\\bigg)=2-a>0$<\/span>&nbsp;suy ra&nbsp;a &lt; 2.<\/p><p>Khi \u0111&oacute; P =&nbsp;a&sup2;&nbsp;&ndash; 2a + 4 = (a&nbsp;&ndash; 1)&sup2; + 3&nbsp;<span class=\"math-tex\">$\\ge$<\/span>&nbsp;3.<\/p><p>Do \u0111&oacute; <span class=\"math-tex\">$P_{min}=3$<\/span>&nbsp;khi a = 1 &lt; 2<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-02-29 02:18:35","option_type":"math","len":0}]}