evaluate the limit. lim_{s→2^{-}} s + |3s - 6| a. 11 b. -1 c. 2 d. 8
evaluate the limit. lim_{s→2^{-}} s + |3s - 6| a. 11 b. -1 c. 2 d. 8
Answer
Explanation:
Step1: Analyze the absolute - value function
When (s\to2^{-}), (3s - 6<0). So, (|3s - 6|=-(3s - 6)=6 - 3s).
Step2: Substitute into the limit expression
The original limit (\lim_{s\to2^{-}}s + |3s - 6|) becomes (\lim_{s\to2^{-}}s+(6 - 3s)).
Step3: Simplify the expression
(\lim_{s\to2^{-}}s + 6-3s=\lim_{s\to2^{-}}(6 - 2s)).
Step4: Evaluate the limit
Substitute (s = 2) into (6 - 2s), we get (6-2\times2=6 - 4 = 2).
Answer:
C. 2