Question

几道大学微积分求极限的题

1，lim(x→∞)｛(x-3)^12(2x+1)^8/(3x-1)^20｝
2，lim(x→+∞)｛(3x³+5x²+4)/[(√x^6)+2]｝
3，lim(x→∞)[x+³√(1-x³)]
4，lim(x→1)｛[√(x+3)-2]/√x-1｝

要过程，不要答案，按情况适当加分

Answer 1

lim(x→∞)｛(x-3)^12(2x+1)^8/(3x-1)^20｝
=lim(x→∞)｛(1-3/x)^12(2+1/x)^8/(3-1/x)^20｝
=2^8/3^20
lim(x→+∞)｛(3x³+5x²+4)/[(√x^6)+2]｝
=lim(x→+∞)｛(3x³+5x²+4)/[(x^3)+2]｝
=3
lim(x→∞)[x+³√(1-x³)]
=lim(x→∞)[x+³√(1-x³)][x^2-x³√(1-x³)+³√(1-x³)^2]/[x^2-x³√(1-x³)+³√(1-x³)^2]
=lim(x→∞)1/[x^2-x³√(1-x³)+³√(1-x³)^2]
=0
lim(x→1)｛[√(x+3)-2]/√x-1}
=lim(x→1)｛[√(x+3)-2][√(x+3)+2]/[√x-1][√(x+3)+2]｝
=lim(x→1)[√x-1]/[√(x+3)+2]
=0