1. lim ln(1+2x) /x , where x trend to 0
2. lim ((ln(x+a)-lna)) /x ,where x trend to 0
3. lim (e^x^4-e^x^3)/5x^3 ,where x trend to 0
limit questions
2011-02-12 11:27 pm
回答 (1)
2011-02-13 1:55 am
✔ 最佳答案
1. lim(x->0) ln(1+2x) /x= lim(x->0) 2/(1+2x)
= 2
2. lim(x->0) ((ln(x+a)-lna)) /x
= lim(x->0) 1/(x+a)
= 1/a
3. lim(x->0) (e^x^4-e^x^3)/5x^3
= lim(x->0) [(4x^3e^x^4)-(3x^2e^x^3)]/(15x^2)
= lim(x->0) [(12x^2+4x^3)e^x^4-(3x^2+6x)e^x^3]/(30x)
= lim(x->0) [(24x+12x^2)e^x^4+(12x^2+4x^3)(4x^3e^x^4)-(6x+6)e^x^3-(3x^2+6x)(3x^2)e^x^3]/30
= -6/30
= -1/5
收錄日期: 2021-04-26 14:04:55
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110212000051KK00756