I know that the answer should be 1, but algebraically, I don't know how to get there. If someone could show me how WITHOUT skipping any steps, I would really appreciate it!
lim (1/x)-(1/(x^2+x))
x --> 0
Can someone show me how to solve this limit problem step by step? I can't figure out the algebra...?
2015-09-07 4:43 pm
回答 (1)
2015-09-07 6:09 pm
✔ 最佳答案
x → 0 , so x ≠ 0( x is close to 0, but never be 0 )
1/x - 1/(x^2+x)
= ( x^2 + x - x ) / [ x(x^2+x) ]
= x^2 / [ x(x^2+x) ]
= x / (x^2+x) , since x ≠ 0
= 1 / (x+1) , since x ≠ 0
Hence,
as x → 0 ,
1/x - 1/(x^2+x)
→ 1 / (x+1)
→ 1 / (0+1)
→ 1
收錄日期: 2021-05-02 14:06:49
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150907084336AAgTQgF