Given that $$F(s)$$ is the one-sided Laplace transform of $$f(t),$$ the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)} d\tau $$ is

If $$f\left( z \right) = {C_0} + {C_1}{z^{ - 1}}\,\,$$ then $$\oint\limits_{|z| = 1} {{{1 + f\left( z \right)} \over z}} \,\,dz$$ is given

If the transfer function of the following network is $$\,{{{V_0}(s)} \over {{V_i}(s)}} = {1 \over {2\, + \,sCR}}$$

The value of the load resistance $${R_L}$$ is

A fully charged mobile phone with a 12 V battery is good for a 10 minute talk-time. Assume that, during the talk-time, the battery delivers a constant current of 2 A and its voltage drops linearly from 12 V to 10 V as shown in the figure. How much energy does the battery deliver during this talk-time?