A.Maths - Limit (easy)

👨🏻‍🏫 學術台數學

2008-02-01 4:18 am

1.
lim(x-->infinity) (x^2 - 1)/(x^2 + 1)

ans=5

2.
lim(h-->0) ((x+h)^3 - x^3)/h

ans=3x^2

3.
lim(x-->infinity) (4x^2 + x + 1)/(3x^2 + 2x + 1 )

ans=4/3

4.
prove:
lim(x-->0) (tan x)/x = 1

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PLEASE SHOW ME THE STEP OF THE CALCULATION

THX!!

更新1:

第4題可唔可以解得詳細d

回答 (1)

用戶3640

2008-02-01 4:35 am

✔ 最佳答案

1.lim(x-->infinity) (x^2 - 1)/(x^2 + 1)=lim(x-->infinity)(1-1/x^2)/(1+1/x^2)=1

2.lim(h-->0) ((x+h)^3 - x^3)/h=lim(h-->0) (3x^2h+3xh^2+h^3)/h
=lim(h-->0) 3x^2+3xh+h^2=3x^2

3.lim(x-->infinity) (4x^2 + x + 1)/(3x^2 + 2x + 1 )
=lim(x-->infinity) (4+1/x+1/x^2)/(3+2/x+1/x^2)=4/3

4.lim(x-->0) (tan x)/x=lim(x-->0) (sinx/x)(1/cosx)=1

參考: me

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