# Each limit represents the derivative of some function f at

Each limit represents the derivative of some function f at some number a. State such an f and a in each case.
$\underset{h\to 0}{lim}\frac{\sqrt{9}+h-3}{h}$
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SlabydouluS62
Remember that:
${f}^{\prime }\left(a\right)=\underset{h\to 0}{lim}\frac{f\left(a+h\right)-f\left(a\right)}{h}$
$\underset{h\to 0}{lim}\frac{\sqrt{9+h}-3}{h}$
Re-write 3 in the numerator as $\sqrt{9}$
$\underset{h\to 0}{lim}\frac{\sqrt{9+h}-\sqrt{9}}{h}$
$\underset{h\to 0}{lim}\frac{f\left(9+h\right)-f\left(9\right)}{h}={f}^{\prime }\left(9\right)$
Where $f\left(x\right)=\sqrt{x}$
Note that a=9

Piosellisf
Is there a solution to this problem?