# Stuck on a STEP function about continuity.

• Sep 20th 2009, 10:58 AM
Arturo_026
Stuck on a STEP function about continuity.
Find the largest value of k for which the function defined by
http://www2.wolframalpha.com/Calcula...=image/gif&s=7
is continuous on the interval [3, 3+k) .

...Through aproximation I found that in order to stay in one "step" the interval has to be [3, <sqrt(10)) but I can't seem to find a way to find k algebraically from the beginning.
• Sep 20th 2009, 11:37 AM
Plato
Quote:

Originally Posted by Arturo_026
Find the largest value of k for which the function defined by
http://www2.wolframalpha.com/Calcula...=image/gif&s=7
is continuous on the interval [3, 3+k) .

...Through aproximation I found that in order to stay in one "step" the interval has to be [3, <sqrt(10)) but I can't seem to find a way to find k algebraically from the beginning.

Well
Because $\displaystyle \left\lfloor {3^2 - 2} \right\rfloor = 7$
we know that $\displaystyle x^2-2<8$
so $\displaystyle x^2<10$.
• Sep 20th 2009, 11:43 AM
Arturo_026
Quote:

Originally Posted by Plato
Well
Because $\displaystyle \left\lfloor {3^2 - 2} \right\rfloor = 7$
we know that $\displaystyle x^2-2<8$
so $\displaystyle x^2<10$.

Right, then i get k < sqrt(10) - 3
Then, what would be the largest value k can attain?