If lim𝑥→2𝑓(𝑥)=3𝑥 and lim𝑥→2𝑔(𝑥)=4𝑥2−5, what is lim𝑥→2𝑔(𝑓(𝑥))?

The given limits are lim𝑥→2𝑓(𝑥)=3𝑥 and lim𝑥→2𝑔(𝑥)=4𝑥2−5.

First, we need to find the limit of f(x) as x approaches 2. According to the given, lim𝑥→2𝑓(𝑥)=3𝑥. If we substitute x=2, we get f(2)=3*2=6.

Next, we need to find the limit of g(f(x)) as x approaches 2. Since we know that f(2)=6, we can substitute this into g(x) to get g(f(2))=g(6).

The given limit for g(x) is lim𝑥→2𝑔(𝑥)=4𝑥2−5. But we need to find g(6), not g(2). So we can't directly use this limit. Instead, we substitute x=6 into the equation to get g(6)=4*6^2-5=139.

Therefore, lim𝑥→2𝑔(𝑓(𝑥))=139.