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n→∞时(n^2+1)sin(3/（n^2-1）)
题目详情
n→∞时(n^2+1)sin(3/（n^2-1）)
▼优质解答
答案和解析
limn→∞(n^2+1)sin(3/（n^2-1）)
=limn→∞(n^2-1+2)sin(3/（n^2-1）)
=limn→∞(n^2-1)sin(3/（n^2-1）)+limn→∞2sin(3/（n^2-1）)
=limn→∞(n^2-1)*3/3sin(3/（n^2-1）)+0
=3limn→∞sin(3/（n^2-1）) / (3/(n^2-1))
=3*1
=3
=limn→∞(n^2-1+2)sin(3/（n^2-1）)
=limn→∞(n^2-1)sin(3/（n^2-1）)+limn→∞2sin(3/（n^2-1）)
=limn→∞(n^2-1)*3/3sin(3/（n^2-1）)+0
=3limn→∞sin(3/（n^2-1）) / (3/(n^2-1))
=3*1
=3
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