arctanx+x趋于正无穷

宁胆娜5167lim(2/π.arctanx)^x当x趋近正无穷的时候值是多少,(^X是指^x次方) -
乔妍苗18760062511 ______[答案] lim(x→∞) (2/π*arctanx)^x =e^lim(x→∞) xln(2/π*arctanx) =e^lim(x→∞) ln(2/π*arctanx)/(1/x) 用洛必达法则得 =e^lim(x→∞) 1/[(x^2+1)arctanx]/(-1/x^2) =e^-lim(x→∞) x^2/[(x^2+1)arctanx] =e^-lim(x→∞) x^2/(x^2*arctanx+arctanx) =e^-lim(x→∞) 1/[arctanx+(arctanx)/x...

宁胆娜5167求极限lim(2/π arctanx)^x 其中x趋向于正无穷大 -
乔妍苗18760062511 ______ 你好!取对数得 lim<x→∞> x ln (2/π arctanx )=lim<x→∞> x ln { 2/π [π/2 - arctan(1/x) ] }= lim<u→0> [ ln (1 - 2/π arctanu ) ] / u 【令u=1/x】= lim<u→0> -2/π arctanu / u 【∵x→0时,ln(1+x) ~ x】= - 2/π 【∵arctanx ~ x】 故原式 = e^(-2/π)

宁胆娜5167求极限有关的函数y=arctanx是否存在极限?若有,是多少,若无,为什么? -
乔妍苗18760062511 ______[答案] x趋近于x0 极限为arctanx0 x趋于正无穷 极限为π/2 x趋于负无穷 极限为-π/2

宁胆娜5167极限求解lim[(2/π)arctanx]^x (x趋向于正的无穷大) -
乔妍苗18760062511 ______[答案] x→+∞lim [(2/π)arctanx]^x=lim e^ln [(2/π)arctanx]^x=e^lim ln[(2/π)arctanx]^x考虑lim ln[(2/π)arctanx]^x=lim x * ln[(2/π)arctanx]=lim ln[1+(2/π)arctanx-1] / (1/x)=lim [(2/π)arctanx-1] / (1/x)该...

宁胆娜5167lim x趋于正无穷 arctanx/x -
乔妍苗18760062511 ______ 0 x趋于正无穷,arctan x 趋向于 π/2 因此原式趋于0

宁胆娜5167lim(2/π.arctanx)^x当x趋近正无穷的时候值是多少? -
乔妍苗18760062511 ______ lim(2/π.arctanx)^x当x趋近正无穷的时候值是e^(-2/π). lim(x→∞) (2/π*arctanx)^x =e^lim(x→∞) xln(2/π*arctanx) =e^lim(x→∞) ln(2/π*arctanx)/(1/x) 用洛必达法则得 =e^lim(x→∞) 1/[(x^2+1)arctanx]/(-1/x^2) =e^-lim(x→∞) x^2/[(x^2+1)arctanx] =e^-lim(x→∞) x^...

宁胆娜5167求极限lim(2/π arctanx)^x 其中x趋向于正无穷大设y=[(2/π)arctanx]^x则:lny=xln[(2/π)arctanx]=x[ln(2/π)+lnarctanx]lim[x→+∞] lny=lim[x→+∞] x[ln(2/π)+lnarctanx]=lim[... -
乔妍苗18760062511 ______[答案] 因为当x->+∞时,arctanx->π/2 所以 [ln(2/π)+lnarctanx] =ln(2/π·arctanx) ->ln(2/π·π/2) =ln1 =0

宁胆娜5167求(2/圆周率·arctanx)^x的极限(X趋向正无穷) -
乔妍苗18760062511 ______[答案] lim(x→∞) (2/π*arctanx)^x=e^lim(x→∞) xln(2/π*arctanx)=e^lim(x→∞) ln(2/π*arctanx)/(1/x)用洛必达法则得=e^lim(x→∞) 1/[(x^2+1)arctanx]/(-1/x^2)=e^-lim(x→∞) x^2/[(x^2+1)arctanx]=e^-lim(x→∞) x...

宁胆娜5167求lim(e^xarctanx )趋于正无穷的极限 -
乔妍苗18760062511 ______[答案] x趋于正无穷的时候, e^x也趋于正无穷, 而arctanx趋于 π/2 所以 lim e^x *arctanx 趋于正无穷乘以常数π, 那么还是趋于正无穷

宁胆娜5167请问,这道高数题,x趋向于正无穷大时,arctanx是否存在极限,若存在,极限值该如何求呢?希望能有具体点的必要的解题. -
乔妍苗18760062511 ______[答案] π/2 arctan反正切的值域 (-π/2, π/2) x 趋于无穷正无穷大时,arctanx的极限存在等于 π/2 x 趋于无穷负无穷大时,arctanx的极限存在等于 -π/2