00:00This chapter is very easy, it is a short list and it is very solid.
00:04But there are some numbers that we call undefined.
00:070 upon 0, infinity upon infinity.
00:100 upon infinity, infinity upon 0.
00:130 to power 0, infinity to power infinity.
00:160 to power infinity, infinity to power infinity.
00:19Today I can't define numbers.
00:22They are all known as undefined numbers.
00:25So, when we come to questions,
00:27we have some basic formulae.
00:31Limit x 10 to 0, sin x upon x equal to 1.
00:35Limit x 10 to 0, 10 x upon x equal to 1.
00:39If we first do here, sin 3 x,
00:44then 1 is not 3.
00:47And if it is 10 to 4 x,
00:49then this is 4.
00:50We have a direct unit.
00:53Direct unit.
00:54We have a direct unit.
00:56Let's see here.
00:57Let's see here.
00:58Let's see here.
00:58Limit x 10 to 0, sin 3 x upon n 4 x.
01:02So, I won't do times higher.
01:04I will say here 3 and here 4,
01:07then the answer will be 3 by 4.
01:09I will save my time.
01:11Now, let's see here.
01:12Let's see here.
01:13Limit x tends to 1.
01:15Okay.
01:16Why did I do this?
01:17Because I put here 0 on x.
01:20So, sin 0 is 0.
01:223 0 is 0.
01:2410 0 is 0.
01:25This is the form of 0.
01:27This is 0 upon 0.
01:29So, this is undefined form.
01:31Look, I should try to keep the limits on the original.
01:35I should try to keep the limits on the original.
01:36I should try to keep the answer 0 or infinity.
01:38But, not in odd answers.
01:41We will save these odd values.
01:44Now, like this is the question.
01:47Limit x tends to 1 under root x minus 1 divided by x minus 1.
01:51How will we solve this?
01:52So, let's take a look.
01:53Let's take a look.
01:55Can I take x to root x square?
01:58This is exactly the problem.
01:59You can cancel the root x square.
02:01You can cancel the root x minus 1.
02:04The root x minus 1 is like this.
02:06This is a square minus b square.
02:08Which is a minus b.
02:10And a plus b.
02:14This will cancel.
02:161 upon root x plus 1.
02:19Let's keep 1.
02:221 upon 1 plus 1.
02:24Final answer 1 upon 2.
02:26Your final answer should be 1 upon 2.
02:29And this is your answer.
