00:01
We are given an equation fx equal to cos x plus 2 sine x plus x square and we have to find the root of this equation using secant method.
00:10
And we have to assume initial value that is x not equal to 0 and x1 equal to minus of 0 .1.
00:18
And this is also given that we have to take four iteration and we have to answer this in four decimal places.
00:26
So first of all initial values are given to us.
00:29
So now the let the number of iteration will be n.
00:32
So n equal to 4 here.
00:35
So now using the second method, we get x of iota plus 1 equal to x iota or we can say x i minus f of x i minus x of i minus 1 divided by f of x i multiplied by f of x i minus 1.
00:57
So, now we will use this where i equal to 1, 2, 3 and 4 because n equal to 4 here.
01:05
Hence, first iteration here x2 equal to x1 minus f of x1 x1 x1 minus x0 divided by f of x1 minus f of x0.
01:26
So we get f of x1 equal to cause of minus of 0 .1 plus of 0 .1 plus 2.
01:35
2 sine of minus of 0 .1 plus minus of 0 .1 to the power 2.
01:41
When we solve this we get f of x1 equal to 0 .9950 plus 2 multiplied by 0 .0998 plus 0 .01.
01:55
So this is 1 .2046.
01:58
Hence now we will find x0.
02:02
So this is cos 0 plus 2 sine 0 plus 2 sine 0 plus 1.
02:06
0 to the power 2 so this is only 1 so now we will use formula so the value gets x to equal to minus of 0 .1 minus of 1 .26 multiplied by minus of 0 .1 this is divided by 1 .2046 minus 1 on solving we get x to equal to 0 .48875 so now we will will use second iteration...