lim x→∞[(x^2+5x)/(x^2-5x)]^(x^k),当k取何值,极限为常数

Lim [x^2/(x^2-1)]^x (x→∞) lim(1+x/x)2x (x→∞) lim(x→∞)arcsin2x/5x lim xsin(2/x) x→∞ lim(x→∞)[(X^2+2x+5)/(3x^2-x+1) = lim(x-cosx)/x x→-∞ lim(x→∞)(cos1/x)^x 1.lim x->∞ （2x/x^2+1)*cosx 2..lim x->∞{ [(x^2-x)arctanx]/x^3-x-5}3..lim x->0 （e^x-e^-x-2x)/(x-sinx) 4..lim x->0 (sinx-x)/(x^3) 5..lim x->0 (x^2*tanx)/(x-tanx) 6..lim x->0 (1+3/x)^2x 7..lim x->0 (1+2x)^(3/sinx) 8.lim x->∞ (x/1+x)^(x-3) 9..li lim(x)lim(x→∞) [(x-1)/(x+1)]^2x 为什么 lim(x->∞) {[(-2)/(x+1)]*2x} = -4 求极限lim(x→∞)(2x/3-x)-(2/3x)求极限lim(x→5)根号(x-1)-2/x-5 lim(x→∞)[5X*(tan2/3x)] lim x→∞ (x+sin 2x)/2 lim(x→∞)(1-2/x)^2x x/2-1lim(1-2/x)x→∞ lim x→∞(2x+1)/(3x-4) lim(x→+∞) (2/π arctan X)^X lim(x→∞)(1-2/x) (x+1)次方 lim x→∞ x-1/x^2