• 2022-06-09
    下列函数中,( )是初等函数.
    A: \(y = \arcsin ({x^2} + 2)\)
    B: \(f(x) = \left\{ \matrix{ 0,x \notin Q \ \cr 1,x \in Q \ \cr} \right.\)
    C: \(y = \sqrt { - {x^2} + 1} \)
    D: \(f(x) = \left\{ \matrix{ {x^2},0 \le x < 1 \ \cr x + 1,x > 1 \ \cr} \right.\)
  • C

    举一反三

    内容

    • 0

      \(x =\)______ 是函数\(f(x) = \left\{ {\matrix{ {x\quad , - 1 \le x \le 1} \cr {1\quad ,x 1} \cr } } \right.\)的跳跃间断点。

    • 1

      设\(f(x) = \left\{ {\matrix{ { { { { e^{2x}} - 1} \over {kx}}\quad ,x &gt; 0} \cr {1 - x\quad ,x \le 0} \cr } } \right.\)在\(x = 0\)处连续,则\(k=\)( )。 A: -1 B: 1 C: -2 D: 2

    • 2

      设函数\(f(x) = \left\{ {\matrix{ { { x^2} - 1\;, - 1 \le x &lt; 0} \cr {x\;\quad \;,0 \le x &lt; 1} \cr {2 - x\;\quad ,1 \le x \le 2} \cr } } \right.\),则下列说法正确的是( )。 A: 在\( x = 0\)及\( x = 1\)处均间断 B: 在\( x = 0\)及\( x = 1\)处均连续 C: 在\( x = 0\)连续,在\( x = 1\)处间断 D: 在\(x = 0\)间断,在\(x = 1\)处连续

    • 3

      曲线$\left\{ \matrix{ {x^2} + {y^2} + {z^2} = 9 \cr y = x \cr} \right.$的参数方程为( ). A: $$\left\{ \matrix{ x = \sqrt 3 \cos t \cr y = \sqrt 3 \cos t \cr z = \sqrt 3 \sin t \cr} \right.(0 \le t \le 2\pi )$$ B: $$\left\{ \matrix{ x = {3 \over {\sqrt 2 }}\cos t\cr y = {3 \over {\sqrt 2 }}\cos t \cr z = 3\sin t \cr} \right.(0 \le t \le 2\pi )$$ C: $$\left\{ \matrix{ x = \cos t\cr y = \cos t\cr z = \sin t \cr} \right.(0 \le t \le 2\pi )$$ D: $$\left\{ \matrix{ x = {{\sqrt 3 } \over 3}\cos t\cr y = {{\sqrt 3 } \over 3}\cos t \cr z = {{\sqrt 3 } \over 3}\sin t\cr} \right.(0 \le t \le 2\pi )$$

    • 4

      \(a = 2\)时,函数\(f(x) = \left\{ {\matrix{ {a\quad \quad ,x = 0} \cr {2 { { \sin x} \over x},x \ne 0} \cr } } \right.\)在\(x = 0\)处连续。( )