evaluate the limit in terms of the constants involved: $lim_{t\rightarrow3}(9t - 4at+5a)=square$

Explanation:

Step1: Apply limit - sum rule

$\lim_{t\rightarrow3}(9t - 4at+5a)=\lim_{t\rightarrow3}(9t)-\lim_{t\rightarrow3}(4at)+\lim_{t\rightarrow3}(5a)$

Step2: Apply constant - multiple rule of limits

$=9\lim_{t\rightarrow3}(t)-4a\lim_{t\rightarrow3}(t) + 5a$

Step3: Evaluate $\lim_{t\rightarrow3}(t)$

Since $\lim_{t\rightarrow c}t = c$, when $c = 3$, we have $\lim_{t\rightarrow3}(t)=3$. So the expression becomes $9\times3-4a\times3 + 5a$

Step4: Simplify the expression

$=27-12a + 5a=27 - 7a$

Answer:

$27 - 7a$