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设函数f(x)=x2+bln(x+1),其中b≠0.(Ⅰ)当时,判断函数f(x)在定义域上...
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设函数f(x)=x
2+bln(x+1),其中b≠0.
(Ⅰ)当
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAjCAYAAAD17ghaAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAE1SURBVFhH7ZbrDcMgDISZjJ1Yh2UYhVFczCs8
rMTQAj+aSFFUNeI+H/YRAYcvcVgf/gjAapBCgra153scMAqEEO4+BeCLNqBegNeBbx0InTw7OA9N
aFRYXCjzGI5zIIwpsFoCQz8DskF8CMUC3bPUKPy0oKVy0zp+sUGIpS8ApBwpn1psokcyQLAf9yla
JTU0sc22ZsSRCID2o3DagvB71JAR4VRNACDsx6ngAtwJp/+oJ0p7gL770YH+5Gr3YKbibg0n33c/
Hp835f9C+NqC1n5/dtPj+EvhqgdyCjKTkD0O6cX8QeIavZmu2WDnM1QOxzEvtnc5gHXZUuYJNnzp
wnKAzqqmwbcDtPmyF4AIvI0A9Gm7DcAoOlm3AHRR7xoxTeJygCrk8lfRlbTLAZ4S6wU47sAHfaF+
kGANFwcAAAAASUVORK5CYII=
)
时,判断函数f(x)在定义域上的单调性;
(Ⅱ)求函数f(x)的极值点;
(Ⅲ)证明对任意的正整数n,不等式
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGkAAAAqCAYAAACwTnX4AAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
都成立.
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设函数f(x)=x2+bln(x+1),其中b≠0.
(Ⅰ)当
时,判断函数f(x)在定义域上的单调性;
(Ⅱ)求函数f(x)的极值点;
(Ⅲ)证明对任意的正整数n,不等式
都成立.
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