• 2022-10-31
    当\( x \to 1 \)时,下列不是无穷小量的是( )。
    A: \( {\left( {x - 1} \right)^2} \)
    B: \( \ln x \)
    C: \( {e^{x - 1}} \)
    D: \( \sin \left( {x - 1} \right) \)
  • C

    举一反三

    内容

    • 0

      \( \sin x \)的麦克劳林公式为( ). A: \( \sin x = x - { { {x^3}} \over {3!}} + { { {x^5}} \over {5!}} - \cdots + {( - 1)^n} { { {x^{2n + 1}}} \over {\left( {2n + 1} \right)!}} + o\left( { { x^{2n + 2}}} \right) \) B: \( \sin x = 1 - { { {x^2}} \over {2!}} + { { {x^4}} \over {4!}} - { { {x^6}} \over {6!}} + \cdots + {( - 1)^n} { { {x^{2n}}} \over {\left( {2n} \right)!}} + o\left( { { x^{2n + 1}}} \right) \) C: \( \sin x = 1 + x + { { {x^2}} \over 2} + \cdots + { { {x^n}} \over {n!}} + o\left( { { x^n}} \right) \)

    • 1

      已知\( y = \ln \left| x \right| \),则\( y' \)为( ). A: \( {1 \over {\left| x \right|}} \) B: \( {1 \over x} \) C: \( - {1 \over x} \) D: \( x \)

    • 2

      \(\lim \limits_{x \to 1} { { \sin \left( { { x^2} - 1} \right)} \over {x - 1}}{\rm{ = }}\)______ 。

    • 3

      \(\int { { {\sec }^{3}}xdx}\)=( ) A: \(\frac{1}{2}\sec x\cot x-\frac{1}{2}\ln \left| \sec x+\tan x \right|+C\) B: \(\frac{1}{2}\sec x\tan x+\frac{1}{2}\ln \left| \sec x+\tan x \right|+C\) C: \(-\frac{1}{2}\csc x\tan x+\frac{1}{2}\ln \left| \sec x-\cot x \right|+C\) D: \(-\frac{1}{2}\sec x\tan x-\frac{1}{2}\ln \left| \csc x+\tan x \right|+C\)

    • 4

      1. $\int \frac{1}{x(1+x)} dx =$ A: \[\ln{(x)}-\ln{\left( x+1\right) }+C\] B: \[\ln{(x)}+\ln{\left( x+1\right) }+C\] C: \[x-\ln{\left( x+1\right) }+C\] D: \[-\ln{(x)}+\ln{\left( x+1\right) }+C\]