Question

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 =

Answer 1

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

Answer 2

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

Answer 3

\[c+2+4=1-c\]

Answer 4

yes but you want them to meet up at one

Answer 5

you want them to match there.

Answer 6

ok but dont the c's cancel out?

Answer 7

\[2c=-5\]
\[c=\frac{-5}{2}=-2.5\]

Answer 8

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

Answer 9

lol thats right haha ty

Answer 10

welcome. helly myininaya

Answer 11

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