{"common":{"save":0,"post_id":"7086","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5253","post_id":"7086","mon_id":"1158924","chapter_id":"1159163","question":"<p>Gi&aacute; tr\u1ecb c\u1ee7a gi\u1edbi h\u1ea1n lim<span class=\"math-tex\">$\\sqrt{n}(\\sqrt{n+1}-\\sqrt{n-1})$<\/span>&nbsp;l&agrave;<\/p>","options":["<strong>A.<\/strong> &ndash;1","<strong>B.<\/strong> <span class=\"math-tex\">$+\\infty$<\/span>","<strong>C.<\/strong> 0","<strong>D.<\/strong> 1"],"correct":"4","level":"3","hint":"","answer":"<p><span class=\"math-tex\">$lim$<\/span>&nbsp;<span class=\"math-tex\">$\\sqrt{n}(\\sqrt{n+1}-\\sqrt{n-1})$<\/span><\/p><p>&nbsp;<span class=\"math-tex\">$=lim\\dfrac{2\\sqrt{n}}{\\sqrt{n+1}+\\sqrt{n-1}}$<\/span><\/p><p>&nbsp;<span class=\"math-tex\">$=lim\\dfrac{2}{\\sqrt{1+\\dfrac{1}{n}}+\\sqrt{1-\\dfrac{1}{n}}}$<\/span><\/p><p><span class=\"math-tex\">$=\\dfrac{2}{2}$<\/span><\/p><p><span class=\"math-tex\">$=1$<\/span><\/p><p>Ch\u1ecdn<span style=\"color:#16a085;\">&nbsp;<strong>D.<\/strong> 1.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-02-29 02:15:28","option_type":"math","len":0},{"id":"5255","post_id":"7086","mon_id":"1158924","chapter_id":"1159163","question":"<p>Gi&aacute; tr\u1ecb c\u1ee7a gi\u1edbi h\u1ea1n&nbsp;<span class=\"math-tex\">$lim$<\/span>&nbsp;<span class=\"math-tex\">$n\\bigg(\\sqrt{n^2+1}-\\sqrt{n^2-3}\\bigg)$<\/span>&nbsp;b\u1eb1ng<\/p>","options":["<strong>A.<\/strong> &ndash;1","<strong>B.<\/strong> 2","<strong>C.<\/strong> 4","<strong>D.<\/strong> <span class=\"math-tex\">$+\\infty$<\/span>"],"correct":"2","level":"3","hint":"","answer":"<p>&nbsp;<span class=\"math-tex\">$lim$<\/span>&nbsp;<span class=\"math-tex\">$n\\bigg(\\sqrt{n^2+1}-\\sqrt{n^2-3}\\bigg)$<\/span>&nbsp;<\/p><p><span class=\"math-tex\">$=lim$<\/span>&nbsp;<span class=\"math-tex\">$\\dfrac{4n}{\\sqrt{n^2+1}+\\sqrt{n^2-3}}$<\/span><\/p><p><span class=\"math-tex\">$=lim\\dfrac{4}{\\sqrt{1+\\dfrac{1}{n^2}}+\\sqrt{1-\\dfrac{3}{n^2}}}$<\/span><\/p><p><span class=\"math-tex\">$=\\dfrac{4}{2}$<\/span><\/p><p><span class=\"math-tex\">$=2$<\/span><\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong> 2.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-02-29 02:20:20","option_type":"math","len":0},{"id":"5256","post_id":"7086","mon_id":"1158924","chapter_id":"1159163","question":"<p>Gi&aacute; tr\u1ecb c\u1ee7a gi\u1edbi h\u1ea1n&nbsp;<span class=\"math-tex\">$lim$<\/span>&nbsp;<span class=\"math-tex\">$n\\bigg(\\sqrt{n^2+n+1}-\\sqrt{n^2+n-6}\\bigg)$<\/span>&nbsp;l&agrave;<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\sqrt{7}-1$<\/span>","<strong>B.<\/strong> 3","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{7}{2}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$+\\infty$<\/span>"],"correct":"3","level":"3","hint":"","answer":"<p>&nbsp;<span class=\"math-tex\">$lim$<\/span>&nbsp;<span class=\"math-tex\">$n\\bigg(\\sqrt{n^2+n+1}-\\sqrt{n^2+n-6}\\bigg)$<\/span>&nbsp;<\/p><p>&nbsp;<span class=\"math-tex\">$=lim\\dfrac{7n}{\\sqrt{n^2+n+1}+\\sqrt{n^2+n-6}}$<\/span><\/p><p><span class=\"math-tex\">$=lim\\dfrac{7}{\\sqrt{1+\\dfrac{1}{n}+\\dfrac{1}{n^2}}+\\sqrt{1+\\dfrac{1}{n}-\\dfrac{6}{n^2}}}$<\/span><\/p><p><span class=\"math-tex\">$=\\dfrac{7}{2}$<\/span><\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong>&nbsp;<span class=\"math-tex\">$\\dfrac{7}{2}$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-02-29 02:30:04","option_type":"math","len":0}]}