State space discretization - Mathematics Stack Exchange If the continuous-time system is bounded input bounded output (BIBO) stable, then so is this exact discretized system If your input is not constant between sampling instances, then you could use a forward Euler discretization ($\dot {x} (kT_s)\approx\frac {1} {T_s} (x_ {k+1}-x_k)$) like @polfosol mentioned in his answer
Proof of Continuous compounding formula - Mathematics Stack Exchange 12 Following is the formula to calculate continuous compounding A = P e^(RT) Continuous Compound Interest Formula where, P = principal amount (initial investment) r = annual interest rate (as a decimal) t = number of years A = amount after time t The above is specific to continuous compounding
Show that the function $f (x, y)$ = $xy$ is continuous. The projection $ (x,y)\mapsto x$ is a linear transformation and in finite dimensional space $\Bbb R^2$ it's continuous The same for the second projection and you know the rest of the story