Evaluate the following limits: $($a$)$ lim x$->2$ f$($x$)$; where f$($x$)=\{\{$x$+1,$ x not equal to $2,$ square root of pie, x$=2\}$ b$.$ Lim t$->0((1/$t$)-(1/$t$^2+1)$ c$.$ lim x$->$ infinite $((2$x$^6)+(45$x$^4)+5)/(3$x$^6)+(500$x$^2)+100$x$+200$