大一微积分题目，需要详细解答，回答的好，另加100。跪求大神！ 求一个微积分题目（回答满意另加100分）
\u5728\u7ebf\u7b49\u5927\u795e\u5e2e\u5fd9\u89e3\u7b54\u51e0\u4e2a\u5fae\u79ef\u5206\u9898\u76ee\uff0c\u9898\u76ee\u5982\u9644\u56fe\u6240\u793a\uff0c\u53ef\u4ee5\u5199\u597d\u53d1\u7167\u7247\u7ed9\u6211\u3002100\u5206\uff01\u53ca\u65f6\u4e14\u5b8c\u5584\u518d\u8ffd\u52a0100\uff011\u3001(2x-1)/(x^2+3x+2)=(2x-1)/[(x+1)(x+2)]=-3/(x+1)+5/(x+2)
\u2234\u222b(2x-1)/(x^2+3x+2)
=\u222b[-3/(x+1)+5/(x+2)]dx
=\u222b[-3/(x+1)]d(x+1)+\u222b[5/(x+2)]d(x+2)
=-3ln|x+1|+5ln|x+2|+C
2\u3001\u5229\u7528\u53d8\u9650\u79ef\u5206\u6c42\u5bfc\u516c\u5f0f\uff1a
d[\u222bf(t)dt]/dx=f[\u03c6(x)]*\u03c6'(x)
d[\u222bsintdt]/dx=sin(x^2)*2x=2xsin(x^2)
\u2234lim[(\u222bsintdt)/x] x->0
=lim{d[\u222bsintdt]/dx}/(dx/dx) \u6d1b\u5fc5\u8fbe\u6cd5\u5219
=lim[2xsin(x^2)/1]
=0
3\u3001\u222b1/x^4*dx
=\u222bx^(-4)dx
=[-1/3*x^(-3)]
=-1/3-0
=-1/3
4\u30015\u4e24\u9898\u7528\u4e8c\u5143\u51fd\u6570\u6781\u9650\u7684\u6d1b\u5fc5\u8fbe\u6cd5\u5219
lim[f(x,y)/g(x,y)]=lim{[f'x(x,y)dx+f'y(x,y)dy]/[g'x(x,y)dx+g'y(x,y)dy]}
\u5176\u4e2d\uff0c\u6781\u9650\u70b9\u4e3a x->x0, y->y0\uff0c\u4e14dx=x-x0, dy=y-y0
\u7b2c4\u9898\uff1alim{[\u221a(xy+4)-2]/(xy)} x->1, y->0
f(x,y)=\u221a(xy+4)-2, g(x,y)=xy; x0=1, y0=0; dx=x-1, dy=y
f'x(x,y)=1/2*y/\u221a(xy+4), f'y(x,y)=1/2*x/\u221a(xy+4)
g'x(x,y)=y, g'y(x,y)=x
\u2234lim{[\u221a(xy+4)-2]/(xy)} x->1, y->0
=lim{[1/2*y/\u221a(xy+4)*dx+1/2*x/\u221a(xy+4)*dy]/[y*dx+x*dy]}
=lim[1/2*1/\u221a(xy+4)]*{[y(x-1)+xy]/[y(x-1)+xy]}
=1/4*lim{[2xy-y]/[2xy-y]}
=1/4
\u7b2c5\u9898\uff1alim[sin(xy)/y] x->1, y->0
f(x,y)=sin(xy), g(x,y)=y; x0=1, y0=0; dx=x-1, dy=y
f'x(x,y)=ycos(xy), f'y(x,y)=xcos(xy)
g'x(x,y)=0, g'y(x,y)=1
\u2234lim[sin(xy)/y] x->1, y->0
=lim{[ycos(xy)*dx+xcos(xy)*dy]/[0*dx+1*dy]}
=limcos(xy)*{[y(x-1)+xy]/[0+y]}
=lim1*{[2xy-y]/y}
=lim(2x-1)*lim(y/y)
=(2-1)*1
=1
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\u2460\u5728\u7740\u624b\u6c42\u6781\u9650\u4ee5\u524d\uff0c\u9996\u5148\u8981\u68c0\u67e5\u662f\u5426\u6ee1\u8db30/0\u6216\u221e/\u221e\u578b\uff0c\u5426\u5219\u6ee5\u7528\u6d1b\u5fc5\u8fbe\u6cd5\u5219\u4f1a\u51fa\u9519\u3002\u5f53\u4e0d\u5b58\u5728\u65f6\uff08\u4e0d\u5305\u62ec\u221e\u60c5\u5f62\uff09\uff0c\u5c31\u4e0d\u80fd\u7528\u6d1b\u5fc5\u8fbe\u6cd5\u5219\uff0c\u8fd9\u65f6\u79f0\u6d1b\u5fc5\u8fbe\u6cd5\u5219\u5931\u6548\uff0c\u5e94\u4ece\u53e6\u5916\u9014\u5f84\u6c42\u6781\u9650\u3002\u6bd4\u5982\u5229\u7528\u6cf0\u52d2\u516c\u5f0f\u6c42\u89e3\u3002
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\u4ee5\u4e0b\u94fe\u63a5\u662f\u5177\u4f53\u8fc7\u7a0b
在需求的价格弹性中，假设价格是自变量P，需求量是因变量Q，
则需求的函数可以写成：Q=f(P)。
需求的价格弹性是指需求量Q的变化百分比与价格P的变化百分比的比值，其计算公式为：
价格弹性=需求量变化的百分比÷价格变化的百分比 即E=（ΔQ/Q）/（ΔP/P）
当价格提升20%时
E=(ΔQ/Q)/0.1 =0.8
则ΔQ/Q=8%, 即需求量变化8%
当价格提升20%时
E=(ΔQ/Q)/0.2 =0.8
则ΔQ/Q=16%， 即需求量变化16%
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