## anonymous 5 years ago For what value of the constant c is the function f continuous on (-infinity,infinity )? Answer to 2 decimal places. http://www.webassign.net/cgi-bin/symimage.cgi?expr=f%28x%29%20%3D%20%7B%28cx%5E2%20%2B%202%20x%20%2B%204%20text%28%20if%20%29%20x%3C1%2Cx%5E3%20-%20cx%20text%28%20if%20%29%20x%3E%3D1%29 c =

1. anonymous

replace x by 1, set them equal and solve for c

2. anonymous

for bothe of them? i thought the first one had to be less than 1

3. anonymous

$c+2+4=1-c$

4. anonymous

yes but you want them to meet up at one

5. anonymous

you want them to match there.

6. anonymous

ok but dont the c's cancel out?

7. anonymous

$2c=-5$ $c=\frac{-5}{2}=-2.5$

8. anonymous

no they don't cancel you add c to both sides

9. anonymous

lol thats right haha ty

10. anonymous

welcome. helly myininaya

11. myininaya

$\lim_{x \rightarrow 1^-}f(x)=\lim_{x \rightarrow 1}(cx^2+2x+4)=c(1)+2(1)+4=c+6$ $\lim_{x \rightarrow 1^+}f(x)=\lim_{x \rightarrow 1}(x^3-cx)=1^3-c(1)=1-c$ defintion of conitniuty tells us that the left limit must equal the right limit hey satellite