Verified answer

We can use L'Hopital's Rule.

Differentiating θ^4 = 4θ³

Differentiating θ³ = 3θ²

Hence,

lim (θ^4 - 1)/(θ³ - 1) =

x→1

lim (4θ³)/(3θ²) =

x→1

lim (4θ)/(3) =

x→1

Thus, limit = (4/3)

Using Hospital's lemma:

lim ((Θ^4 -1)/(Θ^3 -1)) as Θ->1 is equal 4/3.