Evaluate lim𝑥→2(3𝑥3+7𝑥−16) and explain the meaning of this value in the context of our course.

To evaluate the limit of the function as x approaches 2, we simply substitute x = 2 into the function:

lim𝑥→2(3𝑥3+7𝑥−16) = 3(2)^3 + 7(2) - 16 = 3(8) + 14 - 16 = 24 + 14 - 16 = 22

The meaning of this value in the context of a calculus course is that as x gets closer and closer to 2, the value of the function (3𝑥3+7𝑥−16) gets closer and closer to 22. This is the fundamental concept of a limit in calculus.