Determine the constant c that makes f continuous on (-inifinity, infinity).
f(x) = c^2+sin(πx) if x

Question

Determine the constant c that makes f continuous on (-inifinity, infinity).
f(x) = c^2+sin(πx) if x <2
f(x) = cx^2-4 if x ≥2

anonymous · Answer

anyone? I really need help. I haven't been able to figure it out, my answers don't match the correct answer

anonymous · Answer

@mayankdevnani

mayankdevnani · Answer

diificult

mayankdevnani · Answer

put f(4)

anonymous · Answer

it's supposed to be c=2 but i don't get how to get there

anonymous · Answer

are those the pieces of a piece-wise function?  if yes, why are both defined for x<2 ?

anonymous · Answer

oh sorry! i will correct it

anonymous · Answer

since the two pieces differently to the left and to the right of x=2, the y-values must be the same at x=2:
$\Large c^2+sin(\pi \cdot x)=c \cdot x^2-4 $
$\Large c^2+sin(\pi \cdot 2)=c \cdot 2^2-4 $
$\Large c^2=4c-4 $
$\Large c^2-4c+4=0 $
c = 2

anonymous · Answer

sorry, i meant to type:  
since the two pieces are defined differently to the left and right of x=2, ....

anonymous · Answer

thank you so much!