Question

Help please!!(:
Limit problem below...

Answer 1

For what value for the constant C is the function f continuous on (-infty, infty) where:
\[f(x)=\left[\begin{matrix}s^2-C & ,s \in (-\infty,4) \\ Cs+3 & ,s \in [4,\infty)\end{matrix}\right]\]
Find C.

Answer 2

Well, where is the possible discontinuity?

Answer 3

at 4?

Answer 4

@Jemurray3

Answer 5

okay, so what's the value of each part at s = 4?

Answer 6

16 and -3/4 ?

Answer 7

@jemurray3

Answer 8

How do you know that if you haven't found C yet?

Answer 9

I plugged in 4 for s and solved for c?

Answer 10

but it ended up being wrong... @Jemurray3

Answer 11

What do you mean you solved for C? you don't set those things equal to zero... I'm just asking what the top part equals and what the bottom part equals when s = 4.

Answer 12

oh, okay when s=4 the top would be (s)^2-C and the bottom would be c(4)+3

Answer 13

so 16 - C and 4C + 3?

Answer 14

In order for the function to be continuous, those must be the same number. Set them equal and solve for C.

Answer 15

so i would get 13/5?

Answer 16

Oh it was correct! That was easier then i thought... Thank you so much!!!(:

Answer 17

No problem