# Continuity

• October 18th 2010, 06:00 PM
mmfoxall
Continuity
f(x) = cx/2 if x<2 and 4(c^2+2)/6x if x>=2

continuous at x=2.

find the values for c.

I'm not sure how to go about calculating this.. Any help would be greatly appreciated.
• October 19th 2010, 03:10 AM
mr fantastic
Quote:

Originally Posted by mmfoxall
f(x) = cx/2 if x<2 and 4(c^2+2)/6x if x>=2

continuous at x=2.

find the values for c.

I'm not sure how to go about calculating this.. Any help would be greatly appreciated.

You require $\displaystyle \frac{c(2)}{2} = \frac{4(c^2 + 2)}{6(2)}$. Simplify and solve for c.
• October 19th 2010, 03:20 AM
HallsofIvy
In other words, you want the two parts to "match up" at x= 2.