Question

Here's a limit question

lim as x approaches 0

xsin(3/x)+34

This looks like a squeeze theorem problem, is that right?

Answer 1

The first term becomes 0. I don't exactly remember the theorem name but x times bounded function when x moves to zero gives zero as an answer.

Answer 2

Yeah the limit as x approaches 0 of xsin(1/x) (or any number over x inside the sin) =0.

So does that not mean that the limit as x approaches 0 of xsin(3/x)+34 be equal to 34? Because essentially you just do (xsin(3/x)=0)+34=34?

Answer 3

Yes I'm right, it's 34.