limits

Consider the following equation in a 2-D real-space. $$|{x_1}{|^p} + |{x_2}{|^p} = 1$$ for $$p > 0$$ Which of the following statement(s) is/are true.

Let $$X\left( s \right) = {{3s + 5} \over {{s^2} + 10s + 20}}$$ be the Laplace Transform of a signal $$x(t).$$ Then $$\,x\left( {{0^ + }} \right)$$ is

At $$t=0,$$ the function $$f\left( t \right) = {{\sin t} \over t}\,\,$$ has

Given $$f\left( t \right) = {L^{ - 1}}\left[ {{{3s + 1} \over {{s^3} + 4{s^2} + \left( {k - 3} \right)}}} \right].$$ $$\mathop {Lt}\limits_{t \to \propto } \,\,f\left( t \right) =...

The Laplace transform of a function f(t) is F(s) = $$\frac{5s^2+23s+6}{s\left(s^2+2s+2\right)}$$. As $$t\rightarrow\infty$$, f(t) approaches

Let $$Y(s)$$ be the Laplace transform of function $$y(t),$$ then the final value of the function is __________.

$$\mathop {Lim}\limits_{\theta \to 0} \,{{\sin \,m\,\theta } \over \theta },$$ where $$m$$ is an integer, is one of the following :

$$\mathop {Lim}\limits_{x \to \infty } \,x\sin {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle x$}} = \_\_\_\_\_.$$