Signal & System CTFT: Find x(t) from X(ω)

[hquang001]

Homework Statement

Find the CT signal associated with CTFT:

Relevant Equations

.

Given the CTFT X(ω):

and here are my solution to find CT signal x(t) associated with the given CTFT , but i got stuck at the limit part

 

[BvU]

FInd any hints in a table of FTs ?

$\$

 

[hquang001]

FInd any hints in a table of FTs ?

$\$

Oh, my professor never mention this, i will check this and see
Thank you

 

[MathematicalPhysicist]

$\exp(n(jt-1/2))-1\to -1$ as $n\to \infty$ since $\exp(jtn)=\cos(tn)+j\sin(tn)$ and $\exp(-n/2)\to 0$ as $n\to \infty$.

 

[hquang001]

$\exp(n(jt-1/2))-1\to -1$ as $n\to \infty$ since $\exp(jtn)=\cos(tn)+j\sin(tn)$ and $\exp(-n/2)\to 0$ as $n\to \infty$.

Yes i have tried this before, but it didn't match the solution that my professor gave, that's why i ask in here to check