Originally Posted by

**steveo0** I don't quite understand the problem when they ask for the smallest/largest integer in the domain of a function. Am I supposed to take the limit or something?

no ... just determine the domain.

For example:

Find the smallest positive integer in the domain of f(x):

$\displaystyle f(x) = \frac{\sin^2x}{\sqrt{x^2-28x-29}}$

x^2 - 28x - 29 > 0

(x - 29)(x + 1) > 0

x > 29 ... x < -1

so ... what is the smallest positive integer in the domain?

and for this one:

Given $\displaystyle f(x) = x^2 - 27x - 28$, find the largest integer in which $\displaystyle f$ is decreasing.

So I found the derivative, did the sign chart and found that it was decreasing at 13.5. Is this right?

largest **integer**? wouldn't that be 13?

and for this one:

$\displaystyle f(x) = \frac{\sqrt{19x - x^2 - 34}}{e^x}$ has a domain of $\displaystyle [a,b]$. Find $\displaystyle b-a$

So for this one, I found the zero of the top of the fraction, which was 17 and 2, and I made those two the domain, so 17-2 = 15. Is this correct?

correct