# Troubled on some kind of limit problem...

• Oct 2nd 2009, 01:03 PM
frozenflames
Troubled on some kind of limit problem...
http://img185.imageshack.us/img185/2...363451b5ba.png

I can't seem to figure out for what value of the constant c is the function f continuous on negative infinity to positive infinity
• Oct 2nd 2009, 01:45 PM
TheEmptySet
Quote:

Originally Posted by frozenflames
http://img185.imageshack.us/img185/2...363451b5ba.png

I can't seem to figure out for what value of the constant c is the function f continuous on negative infinity to positive infinity

For it to be continous it needs to be continous at b=9

This mean that

$\displaystyle \lim_{b \to 9^-}f(b)=f(9)=\lim_{b \to 9^+}f(b)$

so we need to sove $\displaystyle 9c+5=81c-5 \iff 10=72c \iff c=\frac{5}{32}$
• Oct 2nd 2009, 01:51 PM
frozenflames
Quote:

Originally Posted by TheEmptySet
For it to be continous it needs to be continous at b=9

This mean that

$\displaystyle \lim_{b \to 9^-}f(b)=f(9)=\lim_{b \to 9^+}f(b)$

so we need to sove $\displaystyle 9c+5=81c-5 \iff 10=72c \iff c=\frac{32}{5}$

I think you did the final part of the math wrong. It should be 10/72 not the other way around right?
• Oct 2nd 2009, 04:50 PM
mr fantastic
Quote:

Originally Posted by frozenflames
I think you did the final part of the math wrong. It should be 10/72 not the other way around right?

You shouldn't need re-assurance on how to solve $\displaystyle 10 = 72c$. The typo is obvious.