4. $lim_{x \to 5}(3x^{2}-4x - 1)$

Explanation:

Step1: Apply limit - sum rule

$\lim_{x\rightarrow5}(3x^{2}-4x - 1)=\lim_{x\rightarrow5}(3x^{2})-\lim_{x\rightarrow5}(4x)-\lim_{x\rightarrow5}(1)$

Step2: Apply constant - multiple rule

$=3\lim_{x\rightarrow5}(x^{2})-4\lim_{x\rightarrow5}(x)-\lim_{x\rightarrow5}(1)$

Step3: Use power rule and constant rule

$3\times5^{2}-4\times5 - 1$

Step4: Calculate the result

$3\times25-20 - 1=75-20 - 1=54$

Answer:

$54$