Question

The limit represents the derivative of some function f at some number a. Select an appropriate f(t) and a.
lim_(t->1)(t^3+t-2)/(t-1)

1f(t) = t^3, a = 1
f(t) = t^3 + t, a = 1
f(t) = t - 2, a = 1
f(t) = t - 2, a = -1
f(t) = t^3 + t, a = -1
f(t) = t^3, a = -1
none of these

Answer 1

Lim (t^3 + t - 2)/(t-1) as t ---> 1
= lim((t-1)(t^2 + t + 2)/t-1)
= lim t^2 + t + 2
= 1 + 1 + 2
= 4

Don't see how the rest of your choices tie in with that.