Basic limit of a vector of functions:

Limit[ { (t^2-4)/(t+2), t^2-4,  (2*t+4)/(3*t+6) }, t-> -2 ]

A limit when one of the functions’ limit is undefined:

Limit[ { 1/t, 1, t }, t-> 0 ]

Some examples of derivatives, as a preview and to illustrate other operations applied to vectors of functions

D[ x^2, x ]

D[ {  x^2, x^3, x^4, x^5 }, x ]