Question

大一数学极限题lim(√(x²+5)-3)/√(2x+1)-√5)x→2求极限

Answer 1

lim(x->2) [ √(x²+5)-3] / [√(2x+1)-√5] 分子分母同时乘以 [√(x²+5)+3] * [√(2x+1) +√5]

= lim(x->2) [(x² -4) * (√(2x+1) +√5) ] / [ (2x-4) * (√(x²+5)+3)]

= lim(x->2) [(x+2) * (√(2x+1) +√5) ] / [ 2 * (√(x²+5)+3)]

= 4 * (2√5) / 12 = 2√5 /3