## values for constants making piecewise fcn continuous

Limits, differentiation, related rates, integration, trig integrals, etc.

### values for constants making piecewise fcn continuous

I have the following function:

$f(x)=\left{\begin{array}{ll}ax+b&\mbox{ if }-\infty

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.
nona.m.nona

Posts: 249
Joined: Sun Dec 14, 2008 11:07 pm

nona.m.nona wrote:But I can't figure out the answer for a.

I believe the answer will be that any value for $a$ will be acceptable. It's only the y-intercept that must be a particular value in order for the "ends" to meet at x = 0.

The slope of the straight line, as it approaches from the left, is irrelevant.

stapel_eliz

Posts: 1782
Joined: Mon Dec 08, 2008 4:22 pm

### Re: values for constants making piecewise fcn continuous

stapel_eliz wrote:
nona.m.nona wrote:But I can't figure out the answer for a.

I believe the answer will be that any value for $a$ will be acceptable.

I didn't know I could do that. Thanks!
nona.m.nona

Posts: 249
Joined: Sun Dec 14, 2008 11:07 pm