大一两个微积分数学题100分求答案过程急急急'5.6大题 求一道大一微积分题目答案
\u4e00\u9053\u5927\u4e00\u6570\u5b66\u5fae\u79ef\u5206\u9898\u76ee\uff0c\u6c42\u89e3\u7b54\u5440\uff01\u6025\u6025\u6025\uff0c\u8c22\u4e86\uff01(1) .\u4ee4F(x) = f(x) - x
F(1/2) =f(1/2) - 1/2 =1/2>0
F(1 ) = f(1) -1 =-1<0
\u6240\u4ee5\uff1aF(1/2) *F(1) <0
\u7531\u4ecb\u503c\u5b9a\u7406\uff0c\u5728\u03be\u2208(1/2,1)\uff0c\u5fc5\u6709F(\u03be) = 0
\u65e2\uff1af(\u03be)=\u03be;
(2).\u4ee4F(x) = f(x) -x
F(1/2) =f(1/2) - 1/2 =1/2>0
F(1 ) = f(1) -1 =-1<0
\u6240\u4ee5\uff1aF(1/2) *F(1) <0
\u7531\u4ecb\u503c\u5b9a\u7406\uff0c\u5728\u03be\u2208(1/2,1)\uff0c\u5fc5\u6709F(\u03be) = 0,\u53c8F(0) = 0
\u5728[0,\u03be]\u4e0a\u5bf9F(x)\u7528\u7f57\u5c14\u5b9a\u7406\uff0c\u5b58\u5728\u03b7\u2208(0,\u03be)\uff0c\u4f7f\u5f97F\u2018(\u03be) = 0
\u65e2\uff1af'\uff08\u03b7\uff09= 1
(3).\u4ee4g(x) =exp(-\u03bbx)*F(x)
\u53c8\uff1ag(0) = 0,g(\u03be) = 0.
\u7531\u7f57\u5c14\u5b9a\u7406\uff0c
\u5bf9\u4efb\u610f\u5b9e\u6570\u03bb\uff0c\u5fc5\u5b58\u5728x0\u2208(0,\u03be)\uff0c
\u4f7f\u5f97\uff1ag'(x0) =exp(-\u03bbx0)*[f'(x0) - 1 - \u03bb[f(x0)-x0]] =0
\u53c8exp(-\u03bbx0)>0
\u65e2\uff1af'(x0)-\u03bb[f(x0)-x0]=1
exp\u8868\u793a\u81ea\u7136\u5bf9\u6570\u3002exp(-\u03bbx)\u8868\u793aexp\u7684-\u03bbx \u6b21\u65b9
= -e^(-x)*x^2 + ∫<∞，0> 2x* e^(-x) dx 因为 lim<x-∞> e^(-x) =0
=∫<∞，0> 2x* e^(-x) dx 分步积分法
= -e^(-x)*2*x+ ∫ <∞，0> 2 e^(-x) dx
=∫<∞，0> 2 e^(-x) dx = -2*e^(-x)| <∞，0> = -0 + 2*e^0 =2
5.2
根据微分方程公式
y'+ 1/x *y = e^x /x
y*= C* e^（-∫1/x dx） + e^（-∫1/x dx）* ∫ e^x /x * e^（∫1/x dx）dx
= C/x + 1/x* ∫e^x /x * x dx = C/x + 1/x* ∫e^x dx
= C/x + 1/x* e^x 带入y(1)=0= C + e∴ C=-1
方程为 y =-e/x + 1/x* e^x
6 对整体求导有
带入y=1 有 x-sin(π)=0 ∴ x=0 曲线过（0,1）点
xy'+y= cos(π y^2)*2y*y' ②
带入y=1，x=0 有 1= cos(π)*2*y' y'=-1/2
对②求导有：
2y'+ xy" =cos(π y^2)*(y')^2 - sin(πy^2)*(2y*y')^2 + cos(π y^2)*2y*y"
带入 y'=-1/2 x=0 y=1 有
-1=-1/4 -2 y"
y"=3/8
好多年不做这样的题目了，不过还是能看出来，告你个基本方法：
4.1题 凑微分，把分子凑进d后面；4.2换元积分，令x平方等于t
5.1分部积分 ；5.2一阶线性微分方程 直接套公式后带入初始条件求解
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