利用计算知识搜索引擎WolframAlpha做微积分(快速指南)

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limsin2x/(e^x-1),x-0limarctan(1/x)asx-0+limexp(1/x)asx-0-单侧极限limx^2sin(3/x^2)),x-oolimarctan(x),x--oox趋于oo求导数derivativeof(2x^2+3)sin(x)或derivative(2x^2+3)sin(x)derivative：导数d/dx(2x^2+3)sin(x)分式记号((2x^2+3)sin(x))'撇记号derivativeof(2x^2+3)sin(x)atx=3求一点的导数d/dx(2x^2+3)sin(x)atx=3((2x^2+3)sin(x))'atx=3二阶导数secondderivativeofsin(2x^2+3)2ndderivativesin(2x^2+3)(sin(2x^2+3))''撇记号三阶导数(sin(2x^2+3))'''10阶导数10thderivative1/(1+x)d^10/dx^10(1/(1+x))(exp(x)cos(2x^2))''atx=1x=1处的2阶导数7thderivativeof1/(1+x)at00处的7阶导数参数方程的导数(sin(t))'/(2t^2)'x=2t^2,y=sint的导数：dy/dx(cost)'/(sin2t)'att=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-xe^y的导数:dy/dx求方程的根solvex^3+1.1*x^2+0.9*x-1.4=0解方程求根（包括复根）realrootx^3+1.1*x^2+0.9*x-1.4=0只求实根(realroot)求函数的驻点stationarypointofx^3-2x+3驻点：stationarypoint求函数的极值localminx/(x^2+2)极小值：localminlocalmaxx/(x^2+2)极大值：localmaxlocalmax2sin(2x)^2-(5/2)cos(x/2),x=0topi求指定区间内的极大值求函数的最值globalminof2sin(2x)^2-(5/2)cos(x/2)^2for1=x=3求指定区间内的最小值求曲线的拐点inflectionpointofx/(x^2+2)拐点：inflectionpoint求不定积分integratex^2+sin(x)+1intxarctan(x)求定积分integratex^2+sin(x)+1from0to1int1/sqrt(1-x^2),x=0..1/2求广义积分intxexp(-2x)from0toooint1/(x^2+3),x=-oo..oo求积分变限函数integratetexp(-t)from0tox积分上限函数d/dx(inttexp(-t)from0tox)积分上限函数求导F(x)==integratetexp(-t)fromln(x)tox^2积分变限函数d/dx(integratetexp(-t)fromln(x)tox^2)积分变限函数求导曲线与x轴之间的面积areabetween2-x^2andx-axis曲线y=2-x^2与x轴之间的面积曲线下方的面积areaunder3-x^2曲线y=3-x^2与x轴之间的面积求两曲线之间的面积areabetweenxandx^2曲线y=x与y=x^2之间的面积求两曲线的交点solvex^2=x^3曲线y=x^2与y=x^3的交点求两曲线之间的面积areabetweensin(x)andcos(2x)fromx=0topi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轴之间的区域绕x轴旋转旋转体的体积V=pi*Integrate(x^2-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intsqrt(1+((x^2)')^2),x=1..3曲线y=x^2(1x3)的弧长intsqrt((sin(t^3))'^2+(t)'^2),t=-1..1参数曲线x=sin(t^3),y=t(-1t1)的弧长向量的点积(1,2,4).(-2,3,6)向量的叉积(1,2,4)cross(-2,3,6)求偏导数d/dxsin(x^2+2y)d/dysin(x^2+2y)d/dxsin(x^2+2y)at(1,2)高阶偏导数d/dxd/dxx^3*y^2-3*x*y^3-x*y+1d/dyd/dxx^3*y^2-3*x*y^3-x*y+1隐函数的偏导数-(d/dx(exp(z)-xyz))/(d/dz(exp(z)-xyz))方程e^z=xyz的偏导数：dz/dx向量函数的导数(t^2,4t-3,2t^2-6t)'速度向量函数的二阶导数(t^2,e^t,2t^3)''加速度求梯度gradx^2+cos(2y)delx^2y+cos(xy)+xyz^2求方向导数derivativeofx^2+cos(2y)inthedirection(2,-3)at(1,2)求二元函数的驻点stationarypointofx^3-y^3+3*x^2+3*y^2-9*x求二元函数的极值localmaxx^3-y^3+3*x^2+3*y^2-9*x极大值或maximizex^3-y^3+3*x^2+3*y^2-9*x求二元函数的最值minimize2(xy+2/x+2/y)forx0,y0求条件极值maximizexyonx+y=1maximizexyzon2*(x*y+y*z+z*x)=1,x0,y0,z0maximizesqrt(x^2+y^2+z^2)onz=x^2+y^2andx+y+z=1两个约束条件二重积分intx^2y+x,y=2..4,x=1..3矩形区域intxy,x=1..2,y=1..x先y,后xintxy,y=-1..2,x=y^2..y+2先x,后y三重积分intx,x=0..1,y=0..(1-x)/2,z=0..1-x-2y积分次序:：z,y,x级数求和sum3*(2/5)^n,n=1..oo等比级数求和sum1/n^2,n=1..oop-级数求和sum(-1)^(n+1)/n^2,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seriesxsin(x)toorder5xsinx在x=0处的5阶泰勒公式seriese^xatx=1toorder5e^x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+x^2)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ploty=x^3-x^2-x+1,x=-2..2plotxsinx,arctanx两条曲线隐函数的图形plotx^3+y^3=6xyplotx^3+y^3=6xy,x=-4..4,y=-4..4指定范围plotx^2+y^2=2x,x=y^3+1两条曲线参数曲线parametricplot(t(1-sint),tcost)fromt=-10to10参数方程x=t(1-sint),y=tcost的图形极坐标曲线polarplot1+cost,t=0..2pi极坐标方程r=1+cost的图形曲面作图plotx^2+y^2,-2x2,-2y2plotsqrt(2-x^2-3y^2)来源：