Final Value from Y(s)

Correct Answer

C — 6

Concept and Reasoning

Apply the final-value theorem: y(∞)=lim_{s→0}sY(s). With Y(s)=10(2s+3)/[s(s²+2s+5)], the limit is 10×3/5=6. The poles of sY(s) are in the left half-plane, so the theorem is applicable. Hence option C.

Calculation / Key Relation

y(∞)=lim sY(s)=lim 10(2s+3)/(s²+2s+5)=6

Exam Takeaway

Cancel the integrator through sY(s), then check stability of the remaining poles.

Common Mistake

Do not substitute s=0 directly into Y(s); the final-value theorem uses sY(s).