ycosx平方的周期

俟疤质4583函数y=cosx/(1 - sinx)的单调增区间是 -
强中钓18952365171 ______ y=cosx/(1-sinx)=(cosx/2+sinx/2)(cosx/2-sinx/2)/(cosx/2-sinx/2)^2=(cosx/2+sinx/2)/(cosx/2-sinx/2)=√2sin(x+π/4)/√2cos(x+π/4)=tan(x+π/4) x+π/4单调增区间[Kπ-π/2,Kπ+π/2] x在[Kπ-3π/4,Kπ+π/4]是单调增区间

俟疤质4583已知向量a,b满足lal=1,b=(2,1),且ya+b=0(y∈r)则绝对值y=? -
强中钓18952365171 ______ 设向量a(cosx,sinx)则ya+b=(ycosx+2,ysinx+1)=0,ycosx=-2,ysinx=-1,将最后的那两个算式左右都平方再相加,得y^2=5,y的绝对值是根5

俟疤质4583求e∧ycosx的偏导数 -
强中钓18952365171 ______ f(x,y)=e^y cosx fx=-sinx ·e^y fy=e^y·cosx

俟疤质4583求dy/dx=ycosx的通解 -
强中钓18952365171 ______[答案] 显然,y=0是原方程的解 但y≠0时, ∵dy/dx=ycosx ==>dy/y=cosxdx ==>ln│y│=sinx+ln│C│ (C是积分常数) ==>y=Ce^(sinx) ∴y=Ce^(sinx)也是原方程的解 ∵y=0包含在y=Ce^(sinx)中 故原方程的通解是y=Ce^(sinx).

俟疤质4583求y=cosx这个函数的n介导数 -
强中钓18952365171 ______[答案] y'=-sinx=cos(x+π/2) y＂=-cosx=cos(x+2π/2) y＂'=sinx=cosx(x+3π/2) y＂＂=cosx=cos(x+4π/2) . y^n(x)=cos(x+nπ/2)

俟疤质4583求微分方程y'cosx - ysinx=1满足初值条件y(0)=0的特解? -
强中钓18952365171 ______[答案] 方程化为: (ycosx)'=1 积分:ycosx=x+C 代入y(0)=0, 得:C=0 故y=x/cosx

俟疤质4583求证:Y=cosX的导数是 - sinx的过程如何推导的呀? -
强中钓18952365171 ______[答案] 证明过程如下: cosX的导数=lim[cos(X+德尔塔x)-cosX]/德尔塔x=lim[-2sin(X+德尔塔x/2)*sin(德尔塔x/2)/德尔塔x=-sinX 注:所有lim的条件都是德尔塔x趋近于0 其中用到了和差化积公式以及sin无穷小值=无穷小值

俟疤质4583微分方程y'+ycosx=0通解为? -
强中钓18952365171 ______[答案] ∵y'+ycosx=0 ==>dy/dx+ycosx=0 ==>dy/y=-cosxdx ==>ln│y│=-sinx+ln│C│ (C是积分常数) ==>y=Ce^(-sinx) ∴原方程的通解是 y=Ce^(-sinx) (C是积分常数).

俟疤质4583求偏导:z=(xcosy)/(ycosx)设z=(xcosy)/(ycosx),求z对x和y的偏导,怎么不能把xcosy设为u,ycosx设为V用多元函数的求导法来做? -
强中钓18952365171 ______[答案] 对X求偏导(cosy+ysinx)/(ycosx)^2 对Y求(-xsiny-cosx)/(ycosx)^2

俟疤质4583把曲线ycosx+2y - 1=0先沿x轴向右平移 π 2个单位,再沿y轴向下平移1个单位,得到的曲线方程是( ) -
强中钓18952365171 ______[选项] A. (1-y)sinx+2y-3=0 B. (y-1)sinx+2y-3=0 C. (y+1)sinx+2y+1=0 D. -(y+1)sinx+2y+1=0