limx+0sinx-sinsinx

阳狡蕊969limx趋于0(tanx - sin)/x^3用洛比达法则 -
阮褚枫13341745954 ______[答案] lim (tanx-sinx)/x³ =lim (1/cos²x-cosx)/3x² =lim (2sinx/cos³x+sinx)/6x =lim ((2+4sin²x)/(cosx)^4+cosx)/6 =lim (2+1)/6 =1/2

阳狡蕊969limx趋近于0时,sin(sinx)/x的极限 -
阮褚枫13341745954 ______[答案] 运用等价无穷小代换 x→0,sinx~x lim(x→0)sin(sinx)/x =lim(x→0)sinx/x =1

阳狡蕊969limx - >0 (sinx - x)/xsinx=?请朋友们说下过程吧, -
阮褚枫13341745954 ______[答案] lim(x->0) (sinx-x)/(xsinx) (0/0) =lim(x->0) (cosx-1)/(xcosx + sinx) (0/0) =lim(x->0) -sinx/(-xsinx+2cosx) =0

阳狡蕊969x趋向于0limx - sinx/x+sinx=详细一点谢谢 -
阮褚枫13341745954 ______[答案] 极限下X趋于零, lim(x-sinx)/(x+sinx) =lim(1-cosx)/(1+cosx)(用洛必达法则即可) =0

阳狡蕊969limx→0sinx - sin(sinx)/x^2tanx -
阮褚枫13341745954 ______ lim(x→0)(tanx-sinx)/ln(x2+1) =lim(x→0)(x3/2)/ln(x2+1) tanx-sinx~x3/2 =lim(x→0)(3/2)x2/[2x/(x2+1)] 洛必达法则 =lim(x→0)3x(x2+1)/4 =0

阳狡蕊969limx趋向于0(ln|sinx| - ln|x|)的极限 -
阮褚枫13341745954 ______[答案] =In (sinx除以x),x趋于0.括号里面的上下相等,等于1,所以,整个等于0

阳狡蕊969求极限limx - >0(sinx/x)^(1/x^2) -
阮褚枫13341745954 ______ 先取自然对数 limx->0ln(sinx/x)^(1/x^2) =limx->0(lnsinx-lnx)/x^2(这是0/0型,运用洛必达法则) =limx->0(cosx/sinx-1/x)/2x =limx->0(xcosx-sinx)/(2x^2sinx) =limx->0(cosx-xsinx-cosx)/(4xsinx+2x^2cosx) =limx->0-xsinx/(4xsinx+2x^2cosx) =limx->0-sinx/(4sinx+2xcosx) =limx->0-cosx/(4cosx+2cosx-2xsinx) =-1/6 所以limx->0(sinx/x)^(1/x^2)=e^(-1/6)

阳狡蕊969limx→0x - sinxx2(ex - 1)=___. -
阮褚枫13341745954 ______[答案] 原式= lim x→0 1-cosx ex(x2+2x)-2x= lim x→0 sinx ex(x2+4x+2)-2= lim x→0 cosx ex(x2+6x+6)= 1 6. 故答案为: 1 6.

阳狡蕊969limx - >0(x+sinx)/(x - sinx)等于多少 -
阮褚枫13341745954 ______ limx->0(x+sinx)/(x-sinx)=limx->0 (1+cosx)/(1-cosx) =limx->0-sinx/sinx=-1

阳狡蕊969limx→0sin^2x/x -
阮褚枫13341745954 ______[答案] =lim(x→0)sinx*(sinx/x) =0*1 =0