求lim(x趋于4）根号下1+2x再减去3 /x —2

Question

求lim(x趋于4）根号下1+2x再减去3 /x —2

Answer 1

分母是x-4吧
原式= lim [√(1+2x) -3] / (x-4)
= lim [√(1+2x) -3] [√(1+2x) +3] / (x-4)[√(1+2x) +3]
= lim [(1+2x) -9] / (x-4)[√(1+2x) +3]
= lim 2 / [√(1+2x) +3]
= 1/3