Homework Help: Making a piecewise function continuous

1. Feb 17, 2010

meaganjulie

1. The problem statement, all variables and given/known data

find the values of b and c that make the function f continuous on (-$$\infty$$,$$\infty$$)

f(x) = $$\frac{sin2x}{x}$$ if x< 0
3-3c+b(x+1) if 0$$\leq$$x<2
5-cx+bx^2 if x$$\geq$$ 2
2. Relevant equations

lim as x $$\rightarrow$$ 0- of $$\frac{sin2x}{x}$$
works out to be 0
3. The attempt at a solution

2. Feb 17, 2010

tiny-tim

Welcome to PF!

Hi meaganjulie! Welcome to PF!
Nope

what makes you think that?

3. Feb 17, 2010

meaganjulie

nevermind, that limit is actually 2. the limit for zero from the right also must equal 2, and the right and left limits at x=2 must also match.

thats all ive got.

4. Feb 17, 2010

Char. Limit

Just figure out what c and b values make the first and second equal at x=0.

The other one follows a similar process.

5. Feb 20, 2010

meaganjulie

i dont understand how to find the values for c and b because i dont understand how i can use the point x=0 because the first part of the function has no c or b values. i have to use the last to equations at x=2, but how do i know what that limit is?

6. Feb 21, 2010

tiny-tim

Hi meaganjulie!

(just got up :zzz: …)
The first equation tells you that the limit at x = 0 must be 2.

The second equation tells you conditions on b and c which agree with that limit (at x = 0), and that gives you a formula (in b and c) for the limit at x = 2.

And the third equation tells you conditions on b and c which agree with that limit at x = 2.

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