00:00Good morning, limit x tends to zero root x minus upon root a divided by x minus a.
00:08So dear, now this root x minus root a will be like this.
00:14This can be root x square minus root a square.
00:21This trick is a minus b plus a plus b.
00:26This will be root x minus a.
00:28This will be root x minus root a.
00:33This will be root x plus root a.
00:37This will cancel.
00:39Limit x tends to a.
00:41Now let's put x to a.
00:46So root a plus root a,
00:482 root to a, 1 upon 2 root.
00:51Now let's put it as a short trick.
00:54What do I mean?
00:55I'm going to tell you.
00:58The answer is this.
01:00This is a number.
01:03Limit x tends to a.
01:05What do we do?
01:07We do 7.
01:08We do 7.
01:09Here we do 7.
01:11Here we do 7.
01:11Here we do 7.
01:11What is the answer?
01:121 upon 2 root 7.
01:15If we do 7, there is another number.
01:16We do 3 and 9.
01:18We do 7.
01:18We do 7.
01:18So we have to keep it.
01:20This is a good point.
01:22This is a good point.
01:23Limit x tends to 0,
01:241 plus 2 plus 3,
01:25and then n to divide by n square minus 1.
01:28This is a natural number formula.
01:30n into n plus 1 upon 2.
01:33This is a square minus b square.
01:34Then the fact is n plus 1, n plus 1 cancel.
01:38From here, n upon 2, n minus 1.
01:42Now, my brother,
01:44how much n is the limit?
01:46This limit is n2.
01:47Let's put n here.
01:482 to 2 cancel.
01:502 to 2 cancel.
01:512 minus 1 is 1.
01:511 upon 1 will be equal.
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