已知f(x)={aex,x<0b−1,x=0bx+1,x>0f(x)=\begin{cases}ae^{x},x<0\\b - 1,x = 0\\bx + 1,x>0\end{cases}f(x)=⎩⎨⎧aex,x<0b−1,x=0bx+1,x>0在x=0x = 0x=0处连续,则a=a =a=( ),b=b =b=( )。
若f′(x0)f^\prime(x_0)f′(x0)存在,则limh→0f(x0+h2)−f(x0+2h)h2=\lim\limits_{h\to0}\dfrac{f(x_0 + h^{2}) - f(x_0 + 2h)}{h^{2}} =h→0limh2f(x0+h2)−f(x0+2h)=( ).
(A)f′(x0)−2f′(x0)f'(x_0)-2f'(x_0)f′(x0)−2f′(x0)
(B)2f′(x0)2f'(x_0)2f′(x0)
(C)−2f′(x0)-2f'(x_0)−2f′(x0)
(D)−f′(x0)-f'(x_0)−f′(x0)
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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