# Making a piecewise function continuous

## Homework Statement

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

## Homework Equations

lim as x $$\rightarrow$$ 0- of $$\frac{sin2x}{x}$$
works out to be 0

## The Attempt at a Solution

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tiny-tim
Homework Helper
Welcome to PF!

Hi meaganjulie! Welcome to PF!
lim as x $$\rightarrow$$ 0- of $$\frac{sin2x}{x}$$
works out to be 0
Nope

what makes you think that?

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.

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

The other one follows a similar process.

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?

tiny-tim
Homework Helper
Hi meaganjulie!

(just got up :zzz: …)
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?
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.