## anonymous 3 years ago If possible, choose k so that the following function is continuous on any interval (equation in post).

1. anonymous

$f(x)=\left[\begin{matrix}kcos(x), & x \le0 \\ 10e^{x}-k,&0< x \end{matrix}\right]$

2. anonymous

3. anonymous

I haven't passed 4th grade math yet.

4. anonymous

Oh that's ok then (= thanks anyhow

5. hartnn

do you know the basics of continuity ?

6. anonymous

that the line must contiously go and still be a function (one to one) =P if that's what you mean

7. hartnn

i meant, if f(x) is continuous, at x=0, $\lim \limits{x \rightarrow 0^-} f(x)=\lim \limits{x \rightarrow 0^+f(x)}$

8. hartnn

do you you something like that ^ ?

9. anonymous

|dw:1359178608600:dw|

10. hartnn

for x->0- , since x<0, select k cos x and put x=0 for x->0+ , since x>0, select 10e^x-k and put x=0

11. anonymous

Honestly that is all I know

12. anonymous

uhh...

13. hartnn

when x->0-, lim kcos x = k cos 0 = k when x->0+, lim 10e^x-k = 10e^0-k =10- k for continuity k=10-k can you find k from here ?

14. hartnn

just add k to both sides.