Value of the constant c so piecewise function is continuous

[killasnake]

Hi, I am really lose on this question. What do I solve and How?

For what value of the constant c is the function f continuous on (-infinity, infinity) where

 

[daon]

For it to be continuous,

\(\displaystyle \L Lim_{x->4} (cx+5} = Lim_{x->4} (cx^2-5) \\

\Rightarrow Lim_{x->4} (cx^2-5)-Lim_{x->4} (cx+5) = 0 \\

\Rightarrow Lim_{x->4} [(cx^2-5)-(cx+5)] = 0 \\

\Rightarrow Lim_{x->4} [cx^2 -cx - 10] = 0 \\\)

Now, using what you know from properties of limits, you can plug in 4 to see what the limit should be at 4:

\(\displaystyle \L
\Rightarrow Lim_{x->4} [cx^2 -cx - 10)] = 16c-4c-10 = 12c-10= 0
\\
\Rightarrow c=\frac{5}{6}\)

I'll leave it to you to check.

 

[killasnake]

wow confusing but I somewhat get it...