Question

求极限，高数题，谁能帮帮我，在线等答案!!!!题目在图片里!!!

求极限，要有过程，与内容无关的请不要乱回!!!

Answer 1

解法一:原式=lim(x->5){[x^(1/2)+5^(1/2)]/[x^(2/3)+(5x)^(1/3)+5^(2/3)]}
(分子分母同乘[x^(1/2)+5^(1/2)]*[x^(2/3)+(5x)^(1/3)+5^(2/3)]，再化简)
=[5^(1/2)+5^(1/2)]/[5^(2/3)+(5*5)^(1/3)+5^(2/3)]
=(2/3)/5^(1/6);
解法二:原式=lim(x->5){[(1/3)x^(-2/3)]/[(1/2)x^(-1/2)]}
(0/0型极限，应用罗比达法则)
=[(1/3)*5^(-2/3)]/[(1/2)*5^(-1/2)]
=(2/3)/5^(1/6)。