Question

大一高数想要详细步骤 谢谢

必采纳

Answer 1

如图

Answer 2

1、上下同除以 x^4，得 (x+1/x^3) / (1+1/x^3+1/x^4) = ∞
2、上下同除以 x^5，得 (1+0+0)/(1-0-0) = 1
3、上下同除以 x^5，得 (0+0+0+0)/(1-0+0) = 0
4、上下同除以 x^18，得 (0-2)^5 * (1+0)^13 / [4*(0-1)^18] = 8
5、原式 = lim [(1-2/x)^(x/2)]^2 = e^-2
6、原式 = lim (1-1/x)^x / (1+2/x)^x = e^-1 / e^2 = e^-3
7、直接 = 1
8、原式 = lim 1/4 * (sinx/x) / (sin4x/4x) = 1/4

Answer 3

解：令x^(1/6)=t，则x^(1/3)=t^2，x^(1/2)=t^3，x=t^6，dx=6t^5dt 于是，原式=∫6t^5dt/(t^2+t^3) =6∫t^3dt/(t+1) =6∫[t^2-t+1-1/(t+1)]dt =6(t^3/3-t^2/2+t-ln│t+1│)+C (C是常数) =2t^3-3t^2+6t-6ln│t+1│+C =2x^(1/2)-3x^(1/3)+6x^(1/6)-6ln│x^(1/6)+1│+C。