# Thread: Questions related to limit

1. ## Questions related to limit

I am stuck with this question. I have to calculate the limit

my formula is .. This is final value theorem of Z transform

f(infinity) = limit (z-->1) [ 1- z^ -1] x [ 1/( 1+ z^ -2]

How to solve this

second is

f(infinity) = limit (z-->1) [ 1- z^ -1] x [ z / (( z-1/2) (z-2))]

2. Originally Posted by moonnightingale
I am stuck with this question. I have to calculate the limit

my formula is .. This is final value theorem of Z transform

f(infinity) = limit (z-->1) [ 1- z^ -1] x [ 1/( 1+ z^ -2]

How to solve this

second is

f(infinity) = limit (z-->1) [ 1- z^ -1] x [ z / (( z-1/2) (z-2))]
Both limits as posted are equal to zero.

3. But the answer should not be zero,answer should be infinity atleast for second case.
Kindly see it again

4. Originally Posted by moonnightingale
But the answer should not be zero,answer should be infinity atleast for second case.
Kindly see it again
Both limits as posted are equal to zero.

If you don't like that answer then I suggest you go back and check the calculations that led you to the limits you posted.

5. Originally Posted by mr fantastic
Both limits as posted are equal to zero.

If you don't like that answer then I suggest you go back and check the calculations that led you to the limits you posted.
I am pasting the question

Its solution for Inverse Z transform code is also pasted.
num=[0 1 0]
den=[1 -5/2 1]
x=[1 zeros(1,10)]
y=filter(num,den,x)

If we solve it with inversion integral then answer comes to be

2/3 [2^k - (1/2)^k]

which mean it is ascending continuously
Its initial value is zero which is correct but final value should be infinity

The formula for final value is

x(infinity)= limit (z--->1) (1-1/z) F(z)