I have the following function:
I need to find the values of "a", "b", and "c" that will make this function continuous.
I thought the limit on the third part, as x goes to 0, could be found using the limit from back when we were doing trig derivatives. But using "sin(theta)/theta, as theta goes to 0" won't work, because if theta = 1/x, then theta is actually going to infinity.
On the other hand, 0< 2 + xsin(1/x)<2 + x, since 0<sin(theta)<1 for x "close to" 0. I'm taking this to mean that the limit at 0 is 0, so c = 0.
Then ax + b has to equal 0 at x = 0, so b = 0. But I can't figure out the answer for a.