00:01
In this problem we are given with z is equal to x square minus xy plus 2y square and the point x comma y changes from 1 comma minus 1 to 0 .97 comma minus 0 .95.
00:19
Now we are as to find the value of del z and d z.
00:25
Understand that del z is given by the formula f of a plus a.
00:30
Del x comma b plus del y minus f of a comma b.
00:38
In our case we can assume that a comma b is nothing but 1 comma minus 1.
00:44
So the value of a plus del x comma b plus del y will be the other point what we have here.
00:53
So we can compute the value of del x and del y also.
00:57
Del x will be equal to 0 .97 minus 1 which is nothing but minus 0 .03 and del y is nothing but minus 0 .95 minus of minus plus 1 which is equal to 0 .05.
01:17
Now we need to compute the value of f of 0 .97 comma minus 0 .95 and the value of 5 and the value of f of 0 .97 comma minus 0 .95 and the value of f of f of 1 .5.
01:28
Minus 1.
01:30
If we substitute x is equal to 0 .97 and y is equal to minus 0 .95 in z we will get the value of f of 0 .97 comma minus 0 .95 and it will be equal to 3 .6674.
01:50
Similarly if we substitute x is equal to 1 and y is equal to minus 1 in z we will get the value of f of 1 comma minus 1.
01:59
Be equal to 4.
02:00
So now we can find the value of del z.
02:03
It is nothing but the difference between these two numbers.
02:06
So it will be equal to 3 .6674 minus 4 which is equal to minus 0 .326.
02:16
So this is the answer for the first part of the problem.
02:19
Now we need to compute the value of d z...