diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index ceb72034..9034c3ac 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -599068,6 +599068,46 @@ "space": "4em", "unrelated": [] }, + "022694": { + "id": "022694", + "content": "是否存在正数$a$, 使函数$y=\\dfrac{a^x+1}{2^x}$是偶函数?", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "新教材必修第一册例题", + "edit": [ + "20231107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "022695": { + "id": "022695", + "content": "已知函数$y=f(x)$, $x\\in \\mathbf{R}$, 且当$x\\ge 0$时, $f(x)=2x^3+2^x-1$.\\\\\n(1) 若函数$y=f(x)$是偶函数, 求$f(-2)$;\\\\\n(2) $y=f(x)$是否可能是奇函数? 若可能, 求$f(x)$的表达式; 若不可能, 说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "新教材必修第一册例题", + "edit": [ + "20231107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, "030001": { "id": "030001", "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0