____ lim |6-x - 2x->2----------___|3-x - 1希望大家看得懂..分子:根号下(6-x) - 2分母:根号下(3-x) - 1求极限.............____lim........|6-x - 2 (根号内只有6-x) x->2.......-------- (此为分数线)...........___..........|3-x -
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 00:38:01
![____ lim |6-x - 2x->2----------___|3-x - 1希望大家看得懂..分子:根号下(6-x) - 2分母:根号下(3-x) - 1求极限.............____lim........|6-x - 2 (根号内只有6-x) x->2.......-------- (此为分数线)...........___..........|3-x -](/uploads/image/z/2566746-18-6.jpg?t=____+lim+%7C6-x+-+2x-%3E2----------___%7C3-x+-+1%E5%B8%8C%E6%9C%9B%E5%A4%A7%E5%AE%B6%E7%9C%8B%E5%BE%97%E6%87%82..%E5%88%86%E5%AD%90%3A%E6%A0%B9%E5%8F%B7%E4%B8%8B%286-x%29+-+2%E5%88%86%E6%AF%8D%3A%E6%A0%B9%E5%8F%B7%E4%B8%8B%283-x%29+-+1%E6%B1%82%E6%9E%81%E9%99%90.............____lim........%7C6-x+-+2+%28%E6%A0%B9%E5%8F%B7%E5%86%85%E5%8F%AA%E6%9C%896-x%29+x-%3E2.......--------+%28%E6%AD%A4%E4%B8%BA%E5%88%86%E6%95%B0%E7%BA%BF%29...........___..........%7C3-x+-)
____ lim |6-x - 2x->2----------___|3-x - 1希望大家看得懂..分子:根号下(6-x) - 2分母:根号下(3-x) - 1求极限.............____lim........|6-x - 2 (根号内只有6-x) x->2.......-------- (此为分数线)...........___..........|3-x -
____
lim |6-x - 2
x->2----------
___
|3-x - 1
希望大家看得懂..分子:根号下(6-x) - 2
分母:根号下(3-x) - 1
求极限..
...........____
lim........|6-x - 2 (根号内只有6-x)
x->2.......-------- (此为分数线)
...........___
..........|3-x - 1 (根号内只有3-x)
L'hospital .
____ lim |6-x - 2x->2----------___|3-x - 1希望大家看得懂..分子:根号下(6-x) - 2分母:根号下(3-x) - 1求极限.............____lim........|6-x - 2 (根号内只有6-x) x->2.......-------- (此为分数线)...........___..........|3-x -
辛苦你了,我还是看文字明白的.
把趋向的2代入分子分母,发现都趋向于零,所以使用L'Hospital法则,对分子分母分别求导,然后再把2带进去得到答案1/2
2在不在根号里?
o
这
得1/4
分子分母同乘根号下(3-x)+1
分子变成4-x
分母变成根号下x2-2x+8
把2带进去
((6-x)^(1/2)-2)/((3-x)^(1/2)-1)
=(2-x)*((3-x)^(1/2)+1)/[((6-x)^(1/2)+2)*(2-x)] 分子、分母有理化
=((3-x)^(1/2)+1)/((6-x)^(1/2)+2)
所以
原极限=1/2