已知函数f(x)=x(x+1)(x+1)2f(x)=x(x + 1)(x + 1)^{2}f(x)=x(x+1)(x+1)2,则f(x)f(x)f(x)的单调递增区间是( )
(A)(−∞,−1)(-\infty,-1)(−∞,−1)
(B)(−1,−12)(-1,-\dfrac{1}{2})(−1,−21)
(C)(−14,∞)(-\dfrac{1}{4},\infty)(−41,∞)
(D)[−1,12][-1,\dfrac{1}{2}][−1,21]
设f(x)=2x+3x−2f(x)=2^{x}+3^{x}-2f(x)=2x+3x−2,当x→0x\to0x→0时,有( ).
(A)f(x)f(x)f(x)与xxx等价无穷小
(B)f(x)f(x)f(x)与xxx同阶但非等价无穷小
(C)f(x)f(x)f(x)是比xxx高阶的无穷小
(D)f(x)f(x)f(x)是比xxx低阶的无穷小
下列各组函数相同的是( ).
(A)f(x)=lgx2f(x)=\lg x^{2}f(x)=lgx2与g(x)=2lgxg(x)=2\lg xg(x)=2lgx
(B)f(x)=x−1x−3f(x)=\sqrt{\dfrac{x - 1}{x - 3}}f(x)=x−3x−1与g(x)=x−1x−3g(x)=\dfrac{\sqrt{x - 1}}{\sqrt{x - 3}}g(x)=x−3x−1
(C)f(x)=x4−x33f(x)=\sqrt[3]{x^{4}-x^{3}}f(x)=3x4−x3与g(x)=xx−13g(x)=x\sqrt[3]{x - 1}g(x)=x3x−1
(D)f(x)=xf(x)=xf(x)=x与g(x)=x2g(x)=\sqrt{x^{2}}g(x)=x2
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