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1、利用计算知识搜索引擎WolframAlpha做微积分快速指南说明：点击各个公式进入WolframAlpha网页，然后将其中的函数换成需要计算函数即可。求极限lim sin2x/(ex-1), x-0lim arctan(1/x) as x-0+lim exp(1/x) as x-0-单侧极限lim x2sin(3/x2) , x-oolim arctan(x), x-oo x 趋于oo求导数derivative of (2x2+3)sin(x) 或 derivative (2x2+3)sin(x)derivative：导数d/dx (2x2+3)sin(x) 分式记号(2x2+3)sin(x)
2、撇记号derivative of (2x2+3)sin(x) at x=3求一点的导数d/dx (2x2+3)sin(x) at x=3(2x2+3)sin(x) at x=3二阶导数second derivative of sin(2x2+3)2nd derivative sin(2x2+3)(sin(2x2+3)撇记号三阶导数(sin(2x2+3)10阶导数10th derivative 1/(1+x)d10/dx10(1/(1+x)(exp(x)cos(2x2) at x=1x=1处的2阶导数7th derivative of 1/(1+x) at 00处的7阶导数参数方程的导数(sin
3、(t)/(2t2)x=2t2, y=sint 的导数：dy/dx(cost)/(sin2t) at t=pi/6x=sin2t, y=cost 在 t=pi/6 处的导数隐函数的导数 -( d/dx( 1-x*exp(y)-y ) )/( d/dy( 1-x*exp(y)-y ) )方程 y=1-xey 的导数:dy/dx求方程的根solve x3+1.1*x2+0.9*x-1.4=0解方程求根（包括复根）real root x3+1.1*x2+0.9*x-1.4=0只求实根(real root)求函数的驻点stationary point of x3-2x+3驻点：stationary po
4、int求函数的极值local min x/(x2+2)极小值：local minlocal max x/(x2+2)极大值：local maxlocal max 2sin(2x)2-(5/2)cos(x/2), x=0 to pi求指定区间内的极大值求函数的最值global min of 2sin(2x)2-(5/2)cos(x/2)2 for 1=x=3求指定区间内的最小值求曲线的拐点inflection point of x/(x2+2)拐点：inflection point求不定积分integrate x2+sin(x)+1int xarctan(x)求定积分integrate x2+s
5、in(x)+1 from 0 to 1int 1/sqrt(1-x2) , x= 0 .1/2求广义积分int xexp(-2x) from 0 to ooint 1/(x2+3) , x= -oo . oo求积分变限函数integrate texp(-t) from 0 to x 积分上限函数d/dx ( int texp(-t) from 0 to x ) 积分上限函数求导F(x)=integrate texp(-t) from ln(x) to x2积分变限函数d/dx (integrate texp(-t) from ln(x) to x2 )积分变限函数求导曲线与x轴之间的面积are
6、a between 2-x2 and x-axis曲线y=2-x2与x轴之间的面积曲线下方的面积area under 3-x2曲线y=3-x2与x轴之间的面积求两曲线之间的面积area between x and x2曲线y=x与y=x2之间的面积求两曲线的交点solve x2 = x3曲线y=x2与y=x3的交点求两曲线之间的面积area between sin(x) and cos(2x) from x=0 to pi曲线y=sinx与y=cos2x (0xpi) 之间的面积旋转体的体积V=pi*Integrate (sin(x)2, x=0.2)曲线y=sinx (0x2) 与x轴之间的
7、区域绕x轴旋转旋转体的体积V=pi*Integrate (x2-sin(x)2, x=0.pi)曲线y=x与y=sinx (0xpi) 之间的区域绕x轴旋转求曲线的弧长int sqrt(1+ ( (x2) )2), x=1.3曲线 y=x2 (1x3) 的弧长int sqrt( (sin(t3) 2+(t)2 ), t=-1.1参数曲线 x=sin(t3), y=t(-1t0, y0求条件极值maximize xy on x+y=1maximize xyz on 2*(x*y + y*z + z*x) =1, x0,y0,z0 maximize sqrt(x2+y2+z2) on z=x2+y
8、2 and x+y+z=1两个约束条件二重积分int x2y+x, y=2.4, x=1.3矩形区域int xy , x=1.2, y=1.x先y, 后xint xy , y=-1.2, x=y2.y+2先x, 后y三重积分int x , x=0.1, y=0.(1-x)/2, z=0.1-x-2y积分次序:：z,y,x级数求和sum 3*(2/5)n, n=1.oo等比级数求和sum 1/n2, n=1.oop-级数求和sum (-1)(n+1)/n2, n=1.oo交错级数求和幂级数的和函数sum (-1)(n+1)*x(2n-1)/(2n-1),n=1.oo函数的泰勒公式series x
9、sin(x) to order 5xsinx在x=0处的5阶泰勒公式series ex at x=1 to order 5ex在x=1处的5阶泰勒公式解微分方程y=2xy直接输入微分方程y=e(2x-y), y(0)=0求特解(1+x2)y=2xy, y(0)=1, y(0)=3二阶微分方程的特解高阶线性微分方程 y-5y+6y=xe(2x)通解y+y+sin(2x)=0, y(pi)=1, y(pi)=1特解作图一元函数图形plot y=x3-x2-x+1, x=-2.2plot xsinx,arctanx两条曲线隐函数的图形plot x3+y3=6xyplot x3+y3=6xy, x=-4.4, y=-4.4指定范围plot x2+y2=2x, x=y3+1两条曲线参数曲线parametric plot (t(1-sint),tcost) from t=-10 to 10参数方程 x=t(1-sint), y=tcost 的图形极坐标曲线polar plot 1+cost, t=0.2pi极坐标方程 r=1+cost 的图形曲面作图plot x2+y2, -2x2, -2y2plot sqrt(2-x2-3y2)来源：http:/
