00:01
Hi here for the given question.
00:03
We are given that fx is equal to 39 minus 13 x and it is defined on the interval of 2 to 6 now here for the given question.
00:14
We need to find the value of the limit n tends to infinity for mn here.
00:22
Then geometrically we need to verify this limit also.
00:25
So here in our case, we know that the value of del x will be equal to 6 minus 2 upon n which implies the value of del x is equal to 4 upon n.
00:36
So here we have f of a plus i del x.
00:40
This can be also written as f of 2 plus i of 4 upon n.
00:45
So here our function can be written as this is equal to f of 2 plus i 4 upon n is equal to 39 minus 13 multiplied with 2 plus i 4 upon n.
00:58
So here on further simplifying this we have value equals to 39 minus 26 minus 52 i upon n.
01:09
So here now if we take the value of limit n tends to infinity on both the side f of 2 plus i of 4 upon n.
01:19
So here we have value as limit n tends to infinity here.
01:24
We have delta of summation j running from 0 to n minus 1 13 minus 52 i upon n.
01:33
So here further this can be also written as here.
01:38
We have limit n tends to infinity 4 upon n multiplied with summation of i running from 0 to n minus 1 and here this value is equal to 13 minus 52 i upon n.
01:53
So here further on simplifying this we have 4 upon n multiplied with 13 multiplied with n minus 1 minus 52 divided by n multiplied with 1.
02:09
Here we have 52 divided by n minus 1 multiplied with i.
02:14
So here we have value of limit n tends to infinity.
02:18
So further on simplifying this we can write this as here...