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lim((√x)-√2+√(x-2))/√(x∧2-4)x→2正向趋于2详
题目详情
lim((√x)-√2+√(x-2))/√(x∧2-4) x→2正向趋于2 详
▼优质解答
答案和解析
lim(x->2)[(√x-√2+√(x-2))/√(x²-4)]
=lim(x->2)[(√x-√2)/√(x²-4)+√(x-2)/√(x²-4)]
=lim(x->2)[(x-2)/((√x+√2)√(x²-4))+√(x-2)/√(x²-4)]
=lim(x->2)[√(x-2)/((√x+√2)√(x+2))+1/√(x+2)]
=[√(2-2)/((√2+√2)√(2+2))+1/√(2+2)
=0+1/2
=1/2.
=lim(x->2)[(√x-√2)/√(x²-4)+√(x-2)/√(x²-4)]
=lim(x->2)[(x-2)/((√x+√2)√(x²-4))+√(x-2)/√(x²-4)]
=lim(x->2)[√(x-2)/((√x+√2)√(x+2))+1/√(x+2)]
=[√(2-2)/((√2+√2)√(2+2))+1/√(2+2)
=0+1/2
=1/2.
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