00:01
Hello everyone, this question by using linear approximation we have to find which is larger that is 2 .1 minus root 2 or root 9 .1 minus root 9 by using a linear approximation.
00:16
So first we consider f of x is equal to root x first we consider at x equal to 9.
00:25
Therefore linear approximation l of x is equal to f of g plus f sorry f of 9 plus f dash of 9 x minus 9.
00:38
F of 9 is nothing but root 9 f dash of root 9 will be 1 root x will be 1 by 2 root 9 into x minus so this is 3 this is x by 6 minus 3 by 2 which is equal to 3 by 2 plus x by 6.
01:01
So this is linear approximation.
01:03
So from this we can write root 9 .1 will be f of 9 .1 is approximately l of 9 .1 that is 3 by 2 plus 9 .1 divided by 6 3 .0167.
01:19
Therefore root of 9 .1 minus root 9 is 0 .0167.
01:24
So mark this as 1.
01:25
Next we have to find root 2 .1 minus root 2.
01:29
Similarly we write f of x is equal to root x at x equal to 2.
01:35
Therefore f dash of x will be 1 by 2 root x and the linear approximation will be f of 2 plus f dash of 2 into x minus 2.
01:46
Therefore f dash of 2 is nothing but 1 by 2 root 2 and f of 2 is nothing but root 2...