lim(x趋近于无穷)根号x+2-根号3/x-1

Question

lim(x趋近于无穷)根号x+2-根号3/x-1

Answer 1

属于∞/∞型,应用罗比塔法则分子分母同时求导,得到极限：
= lim(x→∞)[√（x+2）-√3]’/（x-1）’
= lim(x→∞){1/[2√（x+2）]-0}/1
= lim(x→∞)1/[2√（x+2）]
=0
或者分子有理化为：
lim(x→∞)√（x+2）-√3/（x-1）
= lim(x→∞)[√（x+2）-√3][ √（x+2）+√3]/{（x-1）[√（x+2）+√3]}
= lim(x→∞)(x-1)*/{（x-1）[√（x+2）+√3]}
= lim(x→∞)1/[√（x+2）+√3]
=0