Final answer:
The limit of the given expression as t approaches 1 is (1)i + ∞j + sinπk.
Step-by-step explanation:
To find the limit of the given expression, we can evaluate the limit of each component separately. Let's start with the i-component:
limᵗ→¹ (t²-1)/(t-1) = limᵗ→¹ (t+1) = 1.
Next, for the j-component:
limᵗ→¹ (1)/(t²-1) = limᵗ→¹ (1)/((t+1)(t-1)) = ∞.
Finally, for the k-component:
limᵗ→¹ (sinπt)/(lnt) = sinπ.
Therefore, the limit of the given expression as t approaches 1 is (1)i + ∞j + sinπk.