# Continuity of hybrid function - Trying to find the value of c

• September 24th 2011, 01:41 PM
LAPOSH42
Continuity of hybrid function - Trying to find the value of c
Did I do this correct?

determine the values of c such that the function f is continuous on the entire real line

f(x)={x+3 if x less than or equal to 2
cx+6 if x>2

lim x->2+ cx+6=2c+6

lim x->2- x+3=5

2c+6=5
-6 -6
2c/2=-1/2

c=-1/2
• September 24th 2011, 01:48 PM
Plato
Re: Trying to find the value of c
Quote:

Originally Posted by LAPOSH42
Did I do this correct?

determine the values of c such that the function f is continuous on the entire real line

f(x)={x+3 if x less than or equal to 2
cx+6 if x>2

lim x->2+ cx+6=2c+6

lim x->2- x+3=5

2c+6=5
-6 -6
2c/2=-1/2

c=-1/2

That is correct.

Here is some simple LaTeX code
[TEX]\lim _{x \to 2^ + } f(x) = 2c + 6[/TEX] gives $\lim _{x \to 2^ + } f(x) = 2c + 6$