{"common":{"save":0,"post_id":"7085","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5236","post_id":"7085","mon_id":"1158924","chapter_id":"1159163","question":"<p>Có bao nhiêu giá tr\u1ecb nguyên c\u1ee7a tham s\u1ed1 a thu\u1ed9c kho\u1ea3ng (-10 ; 10) \u0111\u1ec3 <span class=\"math-tex\">$lim\\bigg(5n-3(a^2-2)n^3\\bigg)$<\/span> = <span class=\"math-tex\">$-\\infty$<\/span> ?<\/p>","options":["<strong>A.<\/strong> 16","<strong>B.<\/strong> 3","<strong>C.<\/strong> 5","<strong>D.<\/strong> 10"],"correct":"1","level":"2","hint":"","answer":"<p>\u0110\u1ec3 <span class=\"math-tex\">$lim\\bigg(5n-3(a^2-2)n^3\\bigg)$<\/span> = <span class=\"math-tex\">$limn^3\\bigg(\\dfrac{5}{n^2}-3(a^2-2)\\bigg)$<\/span>= <span class=\"math-tex\">$-\\infty$<\/span> <\/p><p>thì <span class=\"math-tex\">$lim\\bigg(\\dfrac{5}{n^2}-3(a^2-2)\\bigg)$<\/span>= <span class=\"math-tex\">$-3(a^2-2)$<\/span> < 0<\/p><p>⇔ <span class=\"math-tex\">$a^2-2>0$<\/span> ⇔ <span class=\"math-tex\">$a<-\\sqrt{2}$<\/span> ho\u1eb7c <span class=\"math-tex\">$a>\\sqrt{2}$<\/span> .<\/p><p>Mà a là s\u1ed1 nguyên thu\u1ed9c kho\u1ea3ng (-10 ; 10) nên<br \/>a ∈ {-9 ; -8 ; -7; - 6 ; -5 ; -4 ; -3 ; -2 ; 2 ; 3 ; 4 ; 5 ; 6 ; 7 ; 8 ; 9}.<\/p><p>V\u1eady có 16 giá tr\u1ecb c\u1ee7a a.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> 16.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-02-28 02:41:55","option_type":"txt","len":0},{"id":"5238","post_id":"7085","mon_id":"1158924","chapter_id":"1159163","question":"<p>Giá tr\u1ecb c\u1ee7a gi\u1edbi h\u1ea1n <span class=\"math-tex\">$lim \\bigg(\\sqrt{n+5}-\\sqrt{n+1}\\bigg)$<\/span> b\u1eb1ng<\/p>","options":["<strong>A.<\/strong> 0","<strong>B.<\/strong> 1","<strong>C.<\/strong> 3","<strong>D.<\/strong> 5"],"correct":"1","level":"2","hint":"","answer":"<p><span class=\"math-tex\">$lim\\bigg(\\sqrt{n+5}-\\sqrt{n+1}\\bigg)$<\/span> = <span class=\"math-tex\">$lim\\dfrac{4}{\\sqrt{n+5}+\\sqrt{n+1}}=0$<\/span><\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> 0.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-02-28 03:01:34","option_type":"txt","len":0},{"id":"5239","post_id":"7085","mon_id":"1158924","chapter_id":"1159163","question":"<p>Giá tr\u1ecb c\u1ee7a gi\u1edbi h\u1ea1n <span class=\"math-tex\">$lim\\bigg(\\sqrt{n^2+2n}-\\sqrt{n^2-2n}\\bigg)$<\/span> là<\/p>","options":["<strong>A.<\/strong> 1","<strong>B.<\/strong> 2","<strong>C.<\/strong> 4","<strong>D.<\/strong> <span class=\"math-tex\">$+\\infty$<\/span>"],"correct":"2","level":"2","hint":"","answer":"<p><span class=\"math-tex\">$lim\\bigg(\\sqrt{n^2+2n}-\\sqrt{n^2-2n}\\bigg)$<\/span> <\/p><p>= <span class=\"math-tex\">$lim\\dfrac{4n}{\\sqrt{n^2+2n}+\\sqrt{n^2-2n}}$<\/span> <\/p><p> <span class=\"math-tex\">$=lim\\dfrac{4}{\\sqrt{1+\\dfrac{2}{n}}+\\sqrt{1-\\dfrac{2}{n^2}}}$<\/span><\/p><p>= 2<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> 2.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-02-28 03:06:10","option_type":"math","len":0}]}
