x→∞时lim[(2n+1)^5(3n-5)^4]/(2n-3)^9=?

求极限lim(x→∞)（1/n+2/n+3/n..+n/n） 求极限lim(-2)^n+3^n/(-2)^[n+1]+3^[n+1] (x→∞) 大学微积分的题目 lim(x→∞)(1^n+2^n+3^n)^1/n x→∞时lim[(2n+1)^5(3n-5)^4]/(2n-3)^9=? 1.7求极限lim(x→∞) [(n+1)(n+2)(n+3)]/5 n^31.7求极限lim(x→∞) [(n+1)(n+2)(n+3)]/5 n^3 计算下列极限：1）lim(n→∞) 1/n3 2）lim(n→∞)4n+1/3n-11）lim(n→∞) 1/n3 2）lim(n→∞)4n+1/3n-13) lim(n→∞) (1/3)n4)lim(n→∞)n3+2n-5/5n3-n 5) lim(n→∞)(1+1/2n)n 6) lim(n→∞)2x3-x2+1/3x2+2x-9 7) lim(x→0 )sin3x/sin7x8) lim((5^n-4^(n-1))/((5^(n+1)+3^(n+2)) n→∞时的极限是多少? 求lim(n→∞)时[5^n-4^(n-1)]/5^(n+1)+3^(n+2) 求极限lim(x→+∞) (x^n/e^x).下面是解题过程：由题可知,当x→+∞时,此极限为∞/∞型,由洛必达法则,得 lim(x→ +∞ )(x^n/e^x)=lim(x→+∞)[nx^(n-1)/e^x)=lim(x→+∞)[n(n-1)x^(n-2)/e^x]=lim(x→+∞)[n(n-2)x^(n-3)/e^x lim x→n (√n+1-√n)*√(n+1/2)lim x n→∞ (√n+1-√n)*√(n+1/2) 求lim n→∞ (1+2/n)^n+3 lim(n→∞)[1-(2n/n+3)] lim(n→∞)(2n-1/n+3) 用数列极限证明lim(n→∞)(n^-2)/(n^+n+1)=1中证明如下:lim(n→∞)3n+1/5n-4 lim (n!+(n-1)!+(n-2)!+(N-3)!+⋯..+2!+1)/n!其中n→∞ 求极限 x→∞lim(3^n+1)/(3^(n+1)+2^n)= lim(x→∞）1+2+3+…+n/(n+2)(n+4)=? lim[n→∞] (x^n+1)^(1/n)