Question

evaluate the limit of lim f(x), where f (x) = 3x -1 if x < 2 and x ^2 + 1 idf x >_ 2

Answer 1

Is f(x) supposed to be a piecewise function? Is x approaching 2? As in\[\lim_{x \rightarrow 2}\left(\begin{matrix}3x+1for x <2 \\ x ^{2}+1for x \ge2\end{matrix}\right)\]

Answer 2

Didn't see a way to write a piecewise function in the equation editor thing so excuse that notation. ;p

Answer 3

I'm going to go with the assumption that what I posted is the question. You have to look at f(x) as x approaches 2 from the left (negative) and the right (positive) and see if they approach the same value. Since both parts of the piecewise function are polynomials (no discontinuities), this is as simple as substituting 2 in for x in both equations and seeing if you get the same result.