A: $\frac12\ln 3$
B: $\ln 3$
C: $\frac{1}{2}$
D: $\frac{1}{2}\ln x$
举一反三
- 函数 $y=\ln \sqrt{x}$的微分为 A: $\frac{1}{2}\ln x dx $ B: $\frac{1}{2}dx$ C: $\frac{1}{2x}dx$ D: $\ln x dx$
- 函数$f(x)=\ln \ln x$的导数是( )。 A: $\frac{1}{x}$ B: $\frac{1}{{{x}^{2}}}$ C: $\frac{1}{\ln x}$ D: $\frac{1}{x\ln x}$
- \(\int { { {\sec }^{3}}xdx}\)=( ) 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: \(-\frac{1}{2}\sec x\tan x-\frac{1}{2}\ln \left| \csc x+\tan x \right|+C\)
- 函数$f(x)=2x^2-\ln x$在下列哪个区间内是单调递增的? A: $(\frac{1}{2},+\infty)$ B: $(0,\frac{1}{2})$ C: $(-\infty,-\frac{1}{2})$ D: $(-\frac{1}{2},\frac{1}{2})$
- 已知函数$y= \ln (1+ x) $,则$y''(x) =$( )。 A: $\frac{1}{(1+x)^2}$ B: $-\frac{1}{(1+x)^2}$ C: $-\frac{1}{1+x}$ D: $\frac{1}{1+x}$
内容
- 0
For the integral $\int_0^{+\infty}\frac{dx}{(x^2+p^2)(x^2+q^2)}$, which of the following statements are CORRECT? A: $\frac{1}{q^2-p^2}[\frac{1}{p}-\frac{1}{q}]\frac{\pi}{2},p>0 \ q>0;$ B: $\frac{1}{q^2-p^2}[\frac{1}{q}+\frac{1}{p}]\frac{\pi}{2}, -p>0 \ -q>0;$ C: $\frac{1}{q^2-p^2}[\frac{1}{p}-\frac{1}{q}]\frac{\pi}{2}, p>0 \ -q>0;$ D: $\frac{1}{p^2-q^2}[\frac{1}{q}+\frac{1}{p}]\frac{\pi}{2}, -p>0 \ q>0.$
- 1
\(已知曲面\Sigma:x^2+y^2+z^2=a^2被平面z=h(0 A: \[2\pi a \ln\frac{a}{h}\] B: \[3\pi a \ln\frac{a}{h}\] C: \[4\pi a \ln\frac{a}{h}\] D: \[\pi a \ln\frac{a}{h}\]
- 2
微分方程$y' = \sqrt{x},y(1)=0$的解为 A: $ \frac{2}{3} x^{\frac{3}{2}} + C $ B: $ \frac{2}{3} x^{\frac{3}{2}} -\frac{2}{3} $ C: $ x^{\frac{3}{2}}-1 $ D: $ x^{\frac{3}{2}}+C $
- 3
下面积分收敛的是 A: $\int_0^\infty \frac{x^{4/3}}{1+x^2} dx$ B: $\int_1^\infty \frac{dx}{x \sqrt[3]{1+x^3}}$ C: $\int_1^\infty \frac{1}{x} dx$ D: $\int_1^\infty \frac{\arctan x}{x} dx$
- 4
函数\(f(x) = x^2,\; x \in [-\pi,\pi]\)的Fourier级数为 A: \(\frac{\pi^2}{3}+4\Sigma_{n=1}^{\infty} \frac{(-1)^n}{n^2} \sin nx ,\; x \in [-\pi,\pi]\) B: \(\frac{\pi^2}{3}+4\Sigma_{n=1}^{\infty} \frac{(-1)^n}{n^2} \cos nx ,\; x \in [-\pi,\pi]\) C: \(\frac{2\pi^2}{3}+4\Sigma_{n=1}^{\infty} \frac{(-1)^n}{n^2} \sin nx ,\; x \in [-\pi,\pi]\) D: \(\frac{2\pi^2}{3}+4\Sigma_{n=1}^{\infty} \frac{(-1)^n}{n^2} \cos nx ,\; x \in [-\pi,\pi]\)