{"common":{"save":0,"post_id":"7091","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5302","post_id":"7091","mon_id":"1158924","chapter_id":"1159163","question":"<p>X&eacute;t t&iacute;nh li&ecirc;n t\u1ee5c c\u1ee7a h&agrave;m s\u1ed1&nbsp;<span class=\"math-tex\">$f(x)=\\begin{cases}\\dfrac{x-1}{\\sqrt{2-x}-1}&amp;\\text{ khi }x &lt; 1\\\\ -2x&amp;\\text{ khi }x \\ge 1\\end{cases}$<\/span>&nbsp;.<br \/>Kh\u1eb3ng \u0111\u1ecbnh n&agrave;o d\u01b0\u1edbi \u0111&acirc;y l&agrave; \u0111&uacute;ng?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$f(x)$<\/span> kh&ocirc;ng li&ecirc;n t\u1ee5c tr&ecirc;n R.","<strong>B.<\/strong> <span class=\"math-tex\">$f(x)$<\/span> kh&ocirc;ng li&ecirc;n t\u1ee5c tr&ecirc;n (0 ; 2).","<strong>C.<\/strong> <span class=\"math-tex\">$f(x)$<\/span> gi&aacute;n \u0111o\u1ea1n t\u1ea1i x = 1.","<strong>D.<\/strong> <span class=\"math-tex\">$f(x)$<\/span> li&ecirc;n t\u1ee5c tr&ecirc;n R."],"correct":"4","level":"2","hint":"","answer":"<p>Ta c&oacute;&nbsp;<span class=\"math-tex\">$f(1)=-2$<\/span>&nbsp;;&nbsp;<span class=\"math-tex\">$\\displaystyle\\lim_{x\\to1^+}f(x)=\\displaystyle\\lim_{x\\to1^+}(-2x)=-2$<\/span>&nbsp;;&nbsp;<span class=\"math-tex\">$\\displaystyle\\lim_{x\\to1^-}f(x)=\\displaystyle\\lim_{x\\to1^-}\\dfrac{x-1}{\\sqrt{2-x}-1}=\\displaystyle\\lim_{x\\to1^-}[-(\\sqrt{2-x}+1)]=-2$<\/span>&nbsp;.<\/p><p>Suy ra&nbsp;<span class=\"math-tex\">$f(x)$<\/span>&nbsp;li&ecirc;n t\u1ee5c t\u1ea1i x = 1.<\/p><p>V\u1eady h&agrave;m s\u1ed1 li&ecirc;n t\u1ee5c tr&ecirc;n R.<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>D.<\/strong>&nbsp;<span class=\"math-tex\">$f(x)$<\/span>&nbsp;li&ecirc;n t\u1ee5c tr&ecirc;n R.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-03 03:32:30","option_type":"math","len":0},{"id":"5306","post_id":"7091","mon_id":"1158924","chapter_id":"1159163","question":"<p>Gi&aacute; tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a a \u0111\u1ec3 h&agrave;m s\u1ed1&nbsp;<span class=\"math-tex\">$f(x)=\\begin{cases}\\dfrac{x^2-5x+6}{\\sqrt{4x-3}-x}&amp;\\text{ khi }{x&gt;3}\\\\{1-a^2x}&amp;\\text{ khi }{x\\le3}\\end{cases}$<\/span>&nbsp; li&ecirc;n t\u1ee5c t\u1ea1i x = 3 l&agrave;<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$-\\dfrac{2}{\\sqrt{3}}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{2}{\\sqrt{3}}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$-\\dfrac{4}{3}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{4}{3}$<\/span>"],"correct":"1","level":"2","hint":"","answer":"<p>\u0110i\u1ec1u ki\u1ec7n b&agrave;i to&aacute;n tr\u1edf th&agrave;nh&nbsp;<span class=\"math-tex\">$\\displaystyle\\lim_{x\\to3^+}f(x)=\\displaystyle\\lim_{x\\to3^-}f(x)=f(3)$<\/span>&nbsp; &nbsp;(*).<\/p><p>Ta c&oacute;&nbsp;<span class=\"math-tex\">$f(3)=1-3a^2$<\/span><\/p><p><span class=\"math-tex\">$\\displaystyle\\lim_{x\\to3^+}f(x)=\\displaystyle\\lim_{x\\to3^+}\\dfrac{x^2-5x+6}{\\sqrt{4x-3}-x}=\\displaystyle\\lim_{x\\to3^+}\\dfrac{(x-2)(\\sqrt{4x-3}+x)}{1-x}=-3$<\/span><\/p><p><span class=\"math-tex\">$\\displaystyle\\lim_{x\\to3^-}f(x)=\\displaystyle\\lim_{x\\to3^-}(1-a^2x)=1-3a^2$<\/span><\/p><p>Khi \u0111&oacute; (*)&nbsp;&hArr;&nbsp;<span class=\"math-tex\">$1-3a^2=-3$<\/span>&nbsp;&hArr;&nbsp;<span class=\"math-tex\">$a=-\\dfrac{2}{\\sqrt{3}}$<\/span>&nbsp;ho\u1eb7c&nbsp;<span class=\"math-tex\">$a=\\dfrac{2}{\\sqrt{3}}$<\/span>&nbsp;.<\/p><p>V\u1eady gi&aacute; tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a a l&agrave;&nbsp;<span class=\"math-tex\">$a=-\\dfrac{2}{\\sqrt{3}}$<\/span>&nbsp;.<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong>&nbsp;<span class=\"math-tex\">$-\\dfrac{2}{\\sqrt{3}}$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-03 03:44:04","option_type":"math","len":0},{"id":"5310","post_id":"7091","mon_id":"1158924","chapter_id":"1159163","question":"<p>T&igrave;m gi&aacute; tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a a \u0111\u1ec3 h&agrave;m s\u1ed1&nbsp;<span class=\"math-tex\">$f(x)=\\begin{cases}\\dfrac{\\sqrt[3]{3x+2}-2}{x-2}&amp;\\text{ khi }{x&gt;2}\\\\{a^2x-\\dfrac{7}{4}}&amp;\\text{ khi }{x\\le2}\\end{cases}$<\/span>&nbsp; li&ecirc;n t\u1ee5c t\u1ea1i x = 2.<\/p>","options":["<strong>A.<\/strong> 3","<strong>B.<\/strong> 0","<strong>C.<\/strong> 1","<strong>D.<\/strong> 2"],"correct":"3","level":"2","hint":"","answer":"<p>Ta c\u1ea7n c&oacute;&nbsp;<span class=\"math-tex\">$\\displaystyle\\lim_{x\\to2^+}f(x)=\\displaystyle\\lim_{x\\to2^-}f(x)=f(2)$<\/span>&nbsp; (*).<\/p><p><span class=\"math-tex\">$f(2)=2a^2-\\dfrac{7}{4}$<\/span><\/p><p><span class=\"math-tex\">$\\displaystyle\\lim_{x\\to2^+}f(x)=\\displaystyle\\lim_{x\\to2^+}\\dfrac{\\sqrt[3]{3x+2}-2}{x-2}$<\/span><\/p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<span class=\"math-tex\">$=\\displaystyle\\lim_{x\\to2^+}\\dfrac{3(x-2)}{(x-2)[(\\sqrt[3]{3x+2})^2+2\\sqrt[3]{3x+2}+4]}$<\/span><\/p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<span class=\"math-tex\">$=\\displaystyle\\lim_{x\\to2^+}\\dfrac{3}{(\\sqrt[3]{3x+2})^2+2\\sqrt[3]{3x+2}+4} $<\/span><\/p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<span class=\"math-tex\">$=\\dfrac{1}{4}$<\/span><\/p><p><span class=\"math-tex\">$\\displaystyle\\lim_{x\\to2^-}f(x)=\\displaystyle\\lim_{x\\to2^-}\\bigg(a^2x-\\dfrac{7}{4}\\bigg)=2a^2-\\dfrac{7}{4}$<\/span><\/p><p>Do \u0111&oacute; (*)&nbsp;&hArr;&nbsp;<span class=\"math-tex\">$2a^2-\\dfrac{7}{4}=\\dfrac{1}{4}$<\/span>&nbsp;&hArr; a = 1 ho\u1eb7c a =&nbsp;&ndash;1.<\/p><p>V\u1eady gi&aacute; tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a a l&agrave; a = 1.<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong> 1.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-06 00:52:05","option_type":"txt","len":0}]}