Final answer:
The limit of the given expression as t approaches 0 is i + j + k.
Step-by-step explanation:
To find the limit of e^(-6t)i + t^2sin^2(t)j + tan(5t)k as t approaches 0, we can evaluate each component separately. The limit of e^(-6t)i as t approaches 0 is e^(0)i = 1i = i. The limit of t^2sin^2(t)j as t approaches 0 is 0j = j. And the limit of tan(5t)k as t approaches 0 is 0k = k. Therefore, the limit of the given expression is i + j + k.