00:01
Hi, the first subdivision a so we can factor out x power 4 from the denominator and numerator.
00:06
So, which gives limit x tends to minus 2 minus so minus 2 x power 6 plus 3 x square plus 2 by x power 4 3 minus 1 by x plus 7 by x power 4.
00:21
So, as x tends to minus 2 minus 1 by x and 1 by x power 4 both tend to minus infinity.
00:37
So we can simplify the expression to limit x tends to minus 2 minus 2 x power 6 plus 3 x square plus 2 by x power 4 into minus infinity which is equal to limit x tends to minus 2 minus minus 2 x power 6 plus 3 x square plus 2 by minus infinity.
01:01
So we can apply l 'hospital's rule 4 times to get.
01:05
So applying l 'hospital's rule limit x tends to minus 2 minus minus 2 x power 6 plus 3 x square plus 2 by minus infinity.
01:24
So, which is equal to we get limit x tends to minus 2 minus minus 432 x power 4 plus 36 x by minus infinity then that is equal to so applying the l 'hospital's rule 4 times we get the answer 0 for the f and subdivision g is subdivision g limit x tends to 0 1 minus cos x by x square.
01:51
So we can use the law limit.
01:53
So x tends to 0 limit law sorry limit x tends to 0 sin x by x is equal to 1 to simplify the expression.
02:06
So this is limit law.
02:12
Therefore, sorry limit x tends to 0 1 minus cos x by x square is equal to limit x tends to 0 2 sin square x by 2 by x square.
02:29
So which is equal to limit x tends to 0 2 into x by 2 the whole square by x square which is equal to limit x tends to 0 1 by 2 which is equal to we get the answer that 1 by 2.
02:47
In the subdivision edge limit x tends to 0 3 x by cos 5 x tan 6 x we can use the limit law in the previous subdivision also...