Chú ý: Để đảm bảo quyền lợi và bảo vệ tài khoản của mình
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{"common":{"save":0,"post_id":"7092","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5321","post_id":"7092","mon_id":"1158924","chapter_id":"1159163","question":"<p>Cho hàm s\u1ed1 <span class=\"math-tex\">$f(x)=\\begin{cases}{-x\\cos x}\\hspace{1cm}\\text{ khi }{x<0}\\\\{\\dfrac{x^2}{1+x}}\\hspace{1.7cm}\\text{ khi }{0\\le x<1}\\\\{x^3}\\hspace{2.5cm}\\text{ khi }{x\\ge1}\\end{cases}$<\/span> . Hàm s\u1ed1 liên t\u1ee5c t\u1ea1i<\/p>","options":["<strong>A.<\/strong> m\u1ecdi \u0111i\u1ec3m x ∈ R.","<strong>B.<\/strong> m\u1ecdi \u0111i\u1ec3m tr\u1eeb x = 0.","<strong>C.<\/strong> m\u1ecdi \u0111i\u1ec3m tr\u1eeb x = 1.","<strong>D.<\/strong> m\u1ecdi \u0111i\u1ec3m tr\u1eeb x = 0; x = 1."],"correct":"3","level":"3","hint":"","answer":"<p>T\u1eadp xác \u0111\u1ecbnh D = R.<\/p><p>D\u1ec5 th\u1ea5y <span class=\"math-tex\">$f(x)$<\/span> liên t\u1ee5c trên m\u1ed7i kho\u1ea3ng <span class=\"math-tex\">$(-\\infty;0);(0;1);(1;+\\infty)$<\/span>.<\/p><p>T\u1ea1i x = 0, ta có <span class=\"math-tex\">$f(0)=0$<\/span> ;<\/p><p><span class=\"math-tex\">$\\displaystyle\\lim_{x\\to0^-}f(x)=\\displaystyle\\lim_{x\\to0^-}(-x\\cos x)=0$<\/span> ;<\/p><p><span class=\"math-tex\">$\\displaystyle\\lim_{x\\to0^+}f(x)=\\displaystyle\\lim_{x\\to0^+}\\dfrac{x^2}{1+x}=0$<\/span> .<\/p><p>Do \u0111ó hàm s\u1ed1 liên t\u1ee5c t\u1ea1i x = 0.<\/p><p>T\u1ea1i x = 1, ta có <span class=\"math-tex\">$f(1)=1$<\/span> ;<\/p><p><span class=\"math-tex\">$\\displaystyle\\lim_{x\\to1^-}f(x)=\\displaystyle\\lim_{x\\to1^-}\\dfrac{x^2}{1+x}=\\dfrac{1}{2}$<\/span> ;<\/p><p><span class=\"math-tex\">$\\displaystyle\\lim_{x\\to1^+}f(x)=\\displaystyle\\lim_{x\\to1^+}x^3=1$<\/span> .<\/p><p>Do \u0111ó hàm s\u1ed1 gián \u0111o\u1ea1n t\u1ea1i x = 1.<\/p><p>V\u1eady hàm s\u1ed1 liên t\u1ee5c t\u1ea1i<span style=\"color:#16a085;\"> <strong>C.<\/strong> m\u1ecdi \u0111i\u1ec3m tr\u1eeb x = 1.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-07 01:14:55","option_type":"txt","len":2},{"id":"5323","post_id":"7092","mon_id":"1158924","chapter_id":"1159163","question":"<p>Cho hàm s\u1ed1 <span class=\"math-tex\">$f(x)=-4x^3+4x-1$<\/span> . M\u1ec7nh \u0111\u1ec1 nào sau \u0111ây là <strong>sai<\/strong>?<\/p>","options":["<strong>A.<\/strong> Hàm s\u1ed1 \u0111ã cho liên t\u1ee5c trên R.","<strong>B.<\/strong> Ph\u01b0\u01a1ng trình <span class=\"math-tex\">$f(x)=0$<\/span> không có nghi\u1ec7m trên kho\u1ea3ng <span class=\"math-tex\">$(-\\infty;1)$<\/span>.","<strong>C.<\/strong> Ph\u01b0\u01a1ng trình <span class=\"math-tex\">$f(x)=0$<\/span> có nghi\u1ec7m trên kho\u1ea3ng <span class=\"math-tex\">$(-2;0)$<\/span>.","<strong>D.<\/strong> Ph\u01b0\u01a1ng trình <span class=\"math-tex\">$f(x)=0$<\/span> có ít nh\u1ea5t hai nghi\u1ec7m trên kho\u1ea3ng <span class=\"math-tex\">$\\bigg(-3;\\dfrac{1}{2}\\bigg)$<\/span>."],"correct":"2","level":"3","hint":"","answer":"<p><strong>A.<\/strong> Hàm s\u1ed1 \u0111ã cho liên t\u1ee5c trên R. (<strong>\u0111úng <\/strong>vì <span class=\"math-tex\">$f(x)$<\/span> là hàm \u0111a th\u1ee9c).<\/p><p>Ta có <span class=\"math-tex\">$f(-1)=-1$<\/span> < 0; <span class=\"math-tex\">$f(-2)=23$<\/span> > 0 nên <span class=\"math-tex\">$f(x)=0$<\/span> có m\u1ed9t nghi\u1ec7m thu\u1ed9c kho\u1ea3ng <span class=\"math-tex\">$(-2;-1)$<\/span> .<\/p><p>L\u1ea1i có <span class=\"math-tex\">$f(0)=-1$<\/span> < 0; <span class=\"math-tex\">$f\\bigg(\\dfrac{1}{2}\\bigg)=\\dfrac{1}{2}$<\/span> > 0 nên <span class=\"math-tex\">$f(x)=0$<\/span> có m\u1ed9t nghi\u1ec7m thu\u1ed9c kho\u1ea3ng <span class=\"math-tex\">$\\bigg(0;\\dfrac{1}{2}\\bigg)$<\/span>.<\/p><p>Vì <span class=\"math-tex\">$(-2;-1)$<\/span> ⊂ <span class=\"math-tex\">$(-2;0)$<\/span> nên <strong>C.<\/strong> Ph\u01b0\u01a1ng trình <span class=\"math-tex\">$f(x)=0$<\/span> có nghi\u1ec7m trên kho\u1ea3ng <span class=\"math-tex\">$(-2;0)$<\/span> là <strong>\u0111úng<\/strong>.<\/p><p>Vì <span class=\"math-tex\">$(-2;-1)$<\/span> ⊂ <span class=\"math-tex\">$\\bigg(-3;\\dfrac{1}{2}\\bigg)$<\/span> và <span class=\"math-tex\">$\\bigg(0;\\dfrac{1}{2}\\bigg)$<\/span> ⊂ <span class=\"math-tex\">$\\bigg(-3;\\dfrac{1}{2}\\bigg)$<\/span> nên <strong>D.<\/strong> Ph\u01b0\u01a1ng trình <span class=\"math-tex\">$f(x)=0$<\/span> có ít nh\u1ea5t hai nghi\u1ec7m trên kho\u1ea3ng <span class=\"math-tex\">$\\bigg(-3;\\dfrac{1}{2}\\bigg)$<\/span> là <strong>\u0111úng<\/strong>.<\/p><p>Vì <span class=\"math-tex\">$(-2;-1)$<\/span> ⊂ <span class=\"math-tex\">$(-\\infty;1)$<\/span> nên <strong>B.<\/strong> Ph\u01b0\u01a1ng trình <span class=\"math-tex\">$f(x)=0$<\/span> không có nghi\u1ec7m trên kho\u1ea3ng <span class=\"math-tex\">$(-\\infty;1)$<\/span> là <span style=\"color:#16a085;\"><strong>sai<\/strong><\/span>.<\/p><p>M\u1ec7nh \u0111\u1ec1 <strong>sai <\/strong>là <span style=\"color:#16a085;\"><strong>B.<\/strong> Ph\u01b0\u01a1ng trình <span class=\"math-tex\">$f(x)=0$<\/span> không có nghi\u1ec7m trên kho\u1ea3ng <span class=\"math-tex\">$(-\\infty;1)$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-07 01:39:29","option_type":"math","len":0},{"id":"5324","post_id":"7092","mon_id":"1158924","chapter_id":"1159163","question":"<p>Cho ph\u01b0\u01a1ng trình <span class=\"math-tex\">$2x^4-5x^2+x+1=0$<\/span>. M\u1ec7nh \u0111\u1ec1 nào sau \u0111ây là <strong>\u0111úng<\/strong>?<\/p>","options":["<strong>A.<\/strong> Ph\u01b0\u01a1ng trình không có nghi\u1ec7m trong kho\u1ea3ng <span class=\"math-tex\">$(-1;1)$<\/span>.","<strong>B.<\/strong> Ph\u01b0\u01a1ng trình không có nghi\u1ec7m trong kho\u1ea3ng <span class=\"math-tex\">$(-2;0)$<\/span>.","<strong>C.<\/strong> Ph\u01b0\u01a1ng trình ch\u1ec9 có m\u1ed9t nghi\u1ec7m trong kho\u1ea3ng <span class=\"math-tex\">$(-2;1)$<\/span>.","<strong>D.<\/strong> Ph\u01b0\u01a1ng trình có ít nh\u1ea5t hai nghi\u1ec7m trong kho\u1ea3ng <span class=\"math-tex\">$(0;2)$<\/span>."],"correct":"4","level":"3","hint":"","answer":"<p>Hàm s\u1ed1 <span class=\"math-tex\">$f(x)=2x^4-5x^2+x+1$<\/span> là hàm \u0111a th\u1ee9c có t\u1eadp xác \u0111\u1ecbnh D = R nên liên t\u1ee5c trên R.<\/p><p>Vì <span class=\"math-tex\">$f(0)=1$<\/span> > 0; <span class=\"math-tex\">$f(-1)=-3$<\/span> < 0 nên <span class=\"math-tex\">$f(x)=0$<\/span> có ít nh\u1ea5t m\u1ed9t nghi\u1ec7m thu\u1ed9c kho\u1ea3ng <span class=\"math-tex\">$(-1;0)$<\/span>.<\/p><p>Mà <span class=\"math-tex\">$(-1;0)$<\/span> ⊂ <span class=\"math-tex\">$(-1;1)$<\/span> và <span class=\"math-tex\">$(-1;0)$<\/span> ⊂ <span class=\"math-tex\">$(-2;0)$<\/span> nên m\u1ec7nh \u0111\u1ec1 <strong>A<\/strong> và <strong>B<\/strong> là <span style=\"color:#c0392b;\"><strong>sai<\/strong><\/span>.<\/p><p>Vì <span class=\"math-tex\">$f(0)=1$<\/span> > 0; <span class=\"math-tex\">$f(1)=-1$<\/span> < 0 nên <span class=\"math-tex\">$f(x)=0$<\/span> có ít nh\u1ea5t m\u1ed9t nghi\u1ec7m thu\u1ed9c kho\u1ea3ng <span class=\"math-tex\">$(0;1)$<\/span>.<\/p><p>Vì <span class=\"math-tex\">$f(1)=-1$<\/span> < 0; <span class=\"math-tex\">$f(2)=15$<\/span> > 0 nên <span class=\"math-tex\">$f(x)=0$<\/span> có ít nh\u1ea5t m\u1ed9t nghi\u1ec7m thu\u1ed9c kho\u1ea3ng <span class=\"math-tex\">$(1;2)$<\/span>.<\/p><p>Mà <span class=\"math-tex\">$(-1;0)$<\/span> ⊂ <span class=\"math-tex\">$(-2;1)$<\/span> và <span class=\"math-tex\">$(0;1)$<\/span> ⊂ <span class=\"math-tex\">$(-2;1)$<\/span> nên m\u1ec7nh \u0111\u1ec1 <strong>C<\/strong> là <span style=\"color:#c0392b;\"><strong>sai<\/strong><\/span>.<\/p><p>M\u1eb7t khác, <span class=\"math-tex\">$(0;1)$<\/span> ⊂ <span class=\"math-tex\">$(0;2)$<\/span> và <span class=\"math-tex\">$(1;2)$<\/span> ⊂ <span class=\"math-tex\">$(0;2)$<\/span> nên m\u1ec7nh \u0111\u1ec1 <strong>D<\/strong> là <span style=\"color:#16a085;\"><strong>\u0111úng<\/strong><\/span>.<\/p><p>M\u1ec7nh \u0111\u1ec1 <strong>\u0111úng<\/strong> là <span style=\"color:#16a085;\"><strong>D.<\/strong> Ph\u01b0\u01a1ng trình có ít nh\u1ea5t hai nghi\u1ec7m trong kho\u1ea3ng <span class=\"math-tex\">$(0;2)$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-07 01:54:22","option_type":"math","len":0}]}