1-x^2

韦狗寿3412(1 - x^2)(2x+1)^5的展开式中x^4的系数 和常数项 -
沃功骂15372298731 ______[答案] (2x+1)^5展开式中:X^2的项与(-X^2)相乘、X^4与1相乘,决定了 展开式中x^4的系数. 则(2x+1)^5展开式中 X^2的项为 C(5,3)*(2X)^2*1^3 = 10* 4X^2 * 1 = 40X^2 X^4的项为 C(5,1)*(2X)^4*1^1 = 5* 16X^4 * 1 = 80X^4 因此展开式中x^4的系数 = 80*1 ...

韦狗寿3412√(1 - x^2) 在0~1的定积分 -
沃功骂15372298731 ______[答案] x=sina dx= cosada x=0,a=0 x=0,a=π/2 √(1-x²)=√cos²a=cosa 原式=∫(0~π/2)cos²ada =∫(0~π/2)(1+cos2a)/2 da =[a/2+1/4*sin2a] (0~π/2) =π/4+0-0-0 =π/4

韦狗寿3412(1 - x^2) ^ - 3/2积分 -
沃功骂15372298731 ______[答案] ∫ (1-x^2)^(-3/2) dx = x(1-x^2)^(-3/2)- 3∫x^2/(1-x^2)^(5/2) dx let x =siny dx = cosy dy ∫x^2/(1-x^2)^(5/2) dx =∫(siny)^2/(cosx)^4 dy =∫(tany)^2 d(tany) =(1/3)( tany)^3 =(1/3)[ x^3/(1-x^2)^(3/2) ] ∫ (1-x^2)^(-3/2) dx = x(1-x^2)^(-3/2)- 3∫x^2/(1-x^2)^(5/2) dx = x(1-x^2)^...

韦狗寿3412求导 y=(arcsinx)/(根号(1 - x^2)) -
沃功骂15372298731 ______[答案] Y'=【(arcsinX)'*√(1-X^2)-(arcsinX)*〔√(1-X^2)〕'】÷(1-X^2)=【〔1÷√(1-X^2)〕*√(1-X^2)-(arcsinX)*〔-X÷√(1-X^2)〕】÷(1-X^2)=〔1+X*(arcsinX)÷√(1-X^2)〕÷(1-X^2)

韦狗寿3412积分x^2 / (1 - x^2) -
沃功骂15372298731 ______ 答:∫[x^2/(1-x^2)]dx=∫[(x^2-1+1)/(1-x^2)]dx=∫[-1+1/(1-x^2)]dx=∫[-1+(1/2)/(1-x)+(1/2)/(1+x)]dx=-x-(1/2)ln|1-x|+(1/2)ln|1+x|+C=(1/2)ln[(1+x)/(1-x)]-x+C

韦狗寿34121/(1 - x^2)不定积分问题不应该是:∫1/(1 - x^2)dx=1/2∫[1/(1 - x)+1/(1+x)]dx=1/2[ln(1 - x)+ln(1+x)]+C=1/2ln[(1+x)/*1 - x)]+C答案部队搞错了,我算的是ln[(1+x)*(1 - x)]为什... -
沃功骂15372298731 ______[答案] =1/2∫[1/(1-x)+1/(1+x)]dx =-1/2∫1/(1-x)d(1-x)+1/2ln(1+x) 【注意这里的1-x放到dx里面前面要加-】 =1/2[ln(1+x)-ln(1-x)]+c =1/2ln(1+x)/(1-x)+c 你算错了-1/2∫1/(1-x)d(1-x),注意看这里的x前面有-号

韦狗寿3412求limx→0(1 - x)^2/x -
沃功骂15372298731 ______[答案] limx→0(1-x)^2/x =limx→0(1+(-x))^(-1/x)*(-2) =[limx→0(1+(-x))^(-1/x)*]^(-2) =e^(-2)

韦狗寿34121/(1 - x^2)幂级数展开式 -
沃功骂15372298731 ______[答案] 1+x^2+x^4+x^6+...+x^2n+...(-1解析看不懂?免费查看同类题视频解析查看解答

韦狗寿3412∫1/x+√(1 - x^2)dx -
沃功骂15372298731 ______[答案] 我想你的题应该是∫1/(x+√(1-x²))dx吧? 令x=sinu,√(1-x²)=cosu,dx=cosudu ∫1/(x+√(1-x²))dx =∫1/(sinu+cosu)*(cosu)du =∫cosu/(sinu+cosu)du =1/2∫(cosu+sinu+cosu-sinu)/(sinu+cosu)du =1/2∫(cosu+sinu)/(sinu+cosu)du+1/2∫(cosu-sinu)/(sinu+cosu)...

韦狗寿34122x^2 - x - 1=0,x等于什么 -
沃功骂15372298731 ______[答案] 2x^2-x-1=0 (x-1)(2x+1)=0 x1=1,x2=-1/2