00:01
Hi, in this question given function f of x equal to x power 6 minus x minus 1, we need to accurate within xx1 equals 0 .3.
00:11
And here given that xa equals 1 and xb equals 2.
00:16
Here we need to use the formula n greater than or equal to log of b minus a divided by epsilon divided by log 2.
00:27
And here given that a equals 1 and b equals 2 and epsilon equals 0 .3.
00:36
On substituting in this, then we get n greater than or equal to log of 2 minus 1 is 1 divided by 0 .3 divided by log 2.
00:48
On further dividing we get greater than or equal to 1 .736, which implies n equals 2.
00:58
That is we round off to 1 .7 to 2.
01:02
So here we need n equal to 2 iterates.
01:05
Consider n equal to 1a equals 1, b equals 2.
01:08
Then c equals a plus b divided by 2.
01:10
So 1 plus 2 divided by 2 which is equal to 1 .5.
01:13
Next we need to find b minus c which is equal to 2 minus 1 .5 which is equal to 0 .5.
01:20
Next we need to find f of c which is equal to f of 1 .5 which is equal to 1 .5 which is equal to 1 .5.
01:29
The whole power 6 minus 1 .5 minus 1.
01:33
On further simplification we get 8 .8906...