anonymous
  • anonymous
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 =
Mathematics
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anonymous
  • anonymous
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 =
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
replace x by 1, set them equal and solve for c
anonymous
  • anonymous
for bothe of them? i thought the first one had to be less than 1
anonymous
  • anonymous
\[c+2+4=1-c\]

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anonymous
  • anonymous
yes but you want them to meet up at one
anonymous
  • anonymous
you want them to match there.
anonymous
  • anonymous
ok but dont the c's cancel out?
anonymous
  • anonymous
\[2c=-5\] \[c=\frac{-5}{2}=-2.5\]
anonymous
  • anonymous
no they don't cancel you add c to both sides
anonymous
  • anonymous
lol thats right haha ty
anonymous
  • anonymous
welcome. helly myininaya
myininaya
  • 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

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