A.maths limit 問題

2010-08-09 2:33 am
1) lim (cos6x-cos2x) / 3x sin 5x
x-->0

2) lim [√2 cos(4x+ π/4)-1]/x
x-->0

3) lim x ln (x^2+3x+2)/(x^2+x)
x-->∞

4) lim [e^(x^2)-e^(x^3)] / (x^2)
x-->0

5) lim [(e^ax)-1] / [(e^bx)-1]
x-->0
更新1:

另加兩題 6) It is given that a function f(x) = x^2 -2 (where x < = 2) and -x +4 (where x > 2) a) Draw the graph of y = f(x) for 0< = x < = 3 b) Determine whether f(x) is continuous at x=2 c) Find lim x->2 f(x)

更新2:

7) It is given that a function g(x) = -2x+4(where x<1) and 3(where x=1) and x+1 (where x>1) a) Draw the graph of y = g(x) for 0 < = x < = 3 b) Determine whether g(x) is continuous at x=1 c) Find lim x -> 1 g(x) 最重要的是兩題的a,因為我不懂畫圖

回答 (2)

2010-08-09 3:12 am
✔ 最佳答案
As follows:


圖片參考:http://i707.photobucket.com/albums/ww74/stevieg90/06-52.jpg



圖片參考:http://i707.photobucket.com/albums/ww74/stevieg90/07-38.jpg



圖片參考:http://i707.photobucket.com/albums/ww74/stevieg90/08-30.jpg


2010-08-08 19:17:13 補充:
By the way, have you learnt "L'Hospital Rule"?
If not, I will change my method to solve the questions.

2010-08-08 19:36:27 補充:
Alternative solution:
Q4: http://i707.photobucket.com/albums/ww74/stevieg90/09-34.jpg
Q5: http://i707.photobucket.com/albums/ww74/stevieg90/10-25.jpg

2010-08-08 22:42:52 補充:
okay....The links of the updated solution for Q4 and Q5 has been uploaded.

2010-08-09 21:45:26 補充:
Do I type Question 3 correctly?

2010-08-09 22:43:51 補充:
lim x ln [(x^2+3x+2)/(x^2+x)]??
x-->∞

2010-08-09 23:08:04 補充:
Sol. of Question 3 has been uploaded.

2010-08-13 14:40:12 補充:
Would you mind asking the new question in a new post?
2010-08-09 6:28 am
No, I haven't learnt this rule.

2010-08-09 21:15:41 補充:
The answer of Q.3 is wrong,the correct answer is 2

2010-08-09 22:08:12 補充:
No, the question is

lim x ln (x^2+3x+2)/(x^2+x)
x-->∞

2010-08-09 22:54:58 補充:
yes, and the question you type is

lim x ln [(x^2+3x+2)/(x^2+2x)]
x-->∞

2010-08-13 14:14:26 補充:
I don't know how to draw the graph for the new questions


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