138 lines
4.0 KiB
Plaintext
138 lines
4.0 KiB
Plaintext
ans
|
||
|
||
023638
|
||
$20\mathrm{m}/\mathrm{s}$
|
||
|
||
019054
|
||
(1) $f'(10)=-10^4$; (2) 实际意义是细菌数量在$t=10$时的瞬时变化率, 它表明在$t=10$附近, 细菌数量大约以每小时$10^4$的速率减少
|
||
|
||
019058
|
||
(1) $-\dfrac{8}{15}{}^\circ\mathrm{C}/\mathrm{min}$; (2) 约$5.95\text{min}$之后($2\sqrt{30}-5$)
|
||
|
||
009905
|
||
(1) $30\mathrm{m}/\mathrm{s}$; (2) $30\mathrm{m}/\mathrm{s}$; (3) $10 a\mathrm{m}/\mathrm{s}$
|
||
|
||
019055
|
||
约$334.2\text{km}/\text{h}$
|
||
|
||
019056
|
||
$x=2$时瞬时变化率为$-3^\circ/\mathrm{h}$, $x=6$时瞬时变化率为$5^\circ/\mathrm{h}$, 意义分别为: 在$2$小时后的这一时刻, 原油温度以每小时$3$摄氏度的速度下降, 在$6$小时后的这一时刻, 原油温度以每小时$5$摄氏度的速度上升
|
||
|
||
021372
|
||
(1)$40\text{m/s}$；(2)$40\text{m/s}$；(3)$10a\text{m/s}$
|
||
|
||
023639
|
||
(1) $1-\sqrt{2}$; (2) 斜率逐渐减小, 并趋近于$-1$
|
||
|
||
019059
|
||
$y=2x-1$
|
||
|
||
019060
|
||
$y=0$
|
||
|
||
019061
|
||
(1) $E,F$; (2) $A,B,C$; (3) $D,B$; (4) $B$; (5) $D$
|
||
|
||
019062
|
||
$(-2,4)$
|
||
|
||
009907
|
||
$y=-6x-3$; $y=6x-3$
|
||
|
||
009908
|
||
(1) 正(图像略); (2) 负(图像略)
|
||
|
||
019064
|
||
$-\dfrac{1}{4}$
|
||
|
||
024841
|
||
(1) $2x^2$; (2) $-x^{-2}$; (3) $\dfrac{1}{2}x^{-\frac{1}{2}}$
|
||
|
||
019065
|
||
$x=\dfrac{\pi}{2}+k\pi$, $k\in \mathbf{Z}$
|
||
|
||
019066
|
||
(1) $y=\dfrac{1}{\mathrm{e}}x$; (2) $y=x-1$, 切点坐标为$(1,0)$
|
||
|
||
009909
|
||
$y'=2x+3$
|
||
|
||
009910
|
||
(1) $f'(x)=\dfrac{2}{3}x^{-\frac{1}{3}}$; (2) $f'(x)=\pi x^{\pi-1}$
|
||
|
||
009911
|
||
$-1$
|
||
|
||
019067
|
||
(1) $y'=2x+1$; (2) $y'=2x-1$
|
||
|
||
023641
|
||
(1) 不存在, 理由略; (2) $b=\pm 2$
|
||
|
||
024840
|
||
$y=2x-1$或$y=10x-25$
|
||
|
||
023643
|
||
$-2$
|
||
|
||
000120
|
||
(1) 偶函数, 理由略; (2) 奇函数, 理由略; (3) 偶函数, 理由略; (4) 既非奇函数又非偶函数, 理由略
|
||
|
||
000121
|
||
$\dfrac{\pi}{6}$
|
||
|
||
000122
|
||
(1) 单调增区间: $[-\dfrac{3\pi}{4}+k\pi,-\dfrac{\pi}{4}+k\pi]$, $k\in \mathbf{Z}$, 单调减区间: $[-\dfrac{\pi}{4}+k\pi,\dfrac{\pi}{4}+k\pi]$, $k\in \mathbf{Z}$;\\
|
||
(2) 单调增区间: $[-\dfrac{5\pi}{6}+2k\pi,\dfrac{\pi}{6}+2k\pi]$, $k\in \mathbf{Z}$, 单调减区间: $[\dfrac{\pi}{6}+2k\pi,\dfrac{7\pi}{6}+2k\pi]$, $k\in \mathbf{Z}$;\\
|
||
(3) 单调增区间: $[-\dfrac{3\pi}{2}+4k\pi,\dfrac{\pi}{2}+4k\pi]$, $k\in \mathbf{Z}$, 单调减区间: $[\dfrac{\pi}{2}+4k\pi,\dfrac{5\pi}{2}+4k\pi]$, $k\in \mathbf{Z}$;\\
|
||
(4) 单调增区间: $(-\dfrac{3\pi}{8}+\dfrac{k\pi}{2},\dfrac{\pi}{8}+\dfrac{k\pi}{2})$, $k\in \mathbf{Z}$
|
||
|
||
000123
|
||
\begin{tikzpicture}[>=latex]
|
||
\draw [->] (-5,0) -- (5,0) node [below] {$x$};
|
||
\draw [->] (0,-2.5) -- (0,2.5) node [left] {$y$};
|
||
\draw (0,0) node [below left] {$O$};
|
||
\draw [domain = -5:5, samples = 200] plot (\x,{2*sin(2*\x/pi*180+60)});
|
||
\draw ({pi/3},0) node [below left = (0 and -0.2)] {$\frac{\pi}{3}$};
|
||
\draw ({5*pi/6},0) node [below right = (0 and -0.2)] {$\frac{5\pi}{6}$};
|
||
\draw ({-pi/6},0) node [above left = (0 and -0.2)] {$-\frac{\pi}{6}$};
|
||
\draw [dashed] ({pi/12},0) --++ (0,2) -- (0,2) node [left] {$2$};
|
||
\end{tikzpicture}
|
||
|
||
000124
|
||
$y=3\sin(3x+\dfrac{\pi}{6})$
|
||
|
||
000125
|
||
(1) 最大值为$0$, 取得最大值的$x$的值为$2k\pi$, $k\in \mathbf{Z}$; 最小值为$-\dfrac{9}{4}$, 取得最小值的$x$的值为$\pm\dfrac{2\pi}{3}+2k\pi$, $k\in \mathbf{Z}$;\\
|
||
(2) 最大值为$1$, 取得最大值的$x$的值为$\dfrac{\pi}{4}$; 最小值为$-1$, 取得最小值的$x$的值为$-\dfrac{\pi}{4}$;\\
|
||
(3) 最大值为$3$, 取得最大值的$x$的值为$-\dfrac{\pi}{4}+k\pi$, $k\in \mathbf{Z}$; 最小值为$-1$, 取得最小值的$x$的值为$\dfrac{\pi}{4}+k\pi$, $k\in \mathbf{Z}$;\\
|
||
(4) 最大值为$1$, 取得最大值的$x$的值为$\dfrac{\pi}{6}$; 最小值为$\dfrac{1}{2}$, 取得最小值的$x$的值为$-\dfrac{\pi}{6}$
|
||
|
||
000126
|
||
(1) 最大问差为$4^\circ$; (2) 在$10$点到$18$点之间实验室需要降温
|
||
|
||
000127
|
||
$\pi$
|
||
|
||
000128
|
||
$(\dfrac{\pi}{4},\dfrac{5\pi}{4})$
|
||
|
||
000129
|
||
(1) 最大值为$\sqrt{2}$, 取得最大值的$x$的值为$\dfrac{3\pi}{8}+k\pi$, $k\in \mathbf{Z}$; (2) 最大值为$\dfrac{1+\sqrt{3}}{2}$, 取得最大值的$x$的值为$\dfrac{4\pi}{3}$
|
||
|
||
000130
|
||
$\dfrac{3}{4}$
|
||
|
||
000135
|
||
$\dfrac{2}{3}$
|
||
|
||
000137
|
||
(1) $f(x)=6-x$; (2) $k=\pm \dfrac{1}{7}$
|
||
|
||
018467
|
||
(1) $A=2$, $\omega = 2$, $\varphi = \dfrac{2\pi}{3}$; (2) 最大值为$\sqrt{3}$, 最小值为$-2$
|
||
|
||
018468
|
||
$(0,\dfrac{3}{4}]$
|
||
|