region-of-convergence

If $u(t)$ is the unit step function, then the region of convergence (ROC) of the Laplace transform of the signal $x(t) = e^{t^2}[u(t-1)-u(t-10)]$ is

The Z-transform of a discrete signal $$x[n]$$ is $$X(z) = {{4z} \over {(z - {1 \over 5})(z - {2 \over 3})(z - 3)}}$$ with $$ROC = R$$. Which one of the following statements is true...

Consider a discrete time signal given by x[n]=(-0.25) n u[n]+(0.5) n u[-n-1] The region of convergence of its Z-transform would be

If $$x\left[ N \right] = {\left( {1/3} \right)^{\left| n \right|}} - {\left( {1/2} \right)^n}\,u\left[ n \right],$$ then the region of convergence $$(ROC)$$ of its $$Z$$-transform...