the limit $\lim_{h \to 0}\dfrac{\sqrt{81+h}-9}{h}$ represents the derivative of some function $f(x)$ at some number a. Find $f$ and $a$.
I don't quite understand what this question is asking. Is it asking about the derivative of this limit? that would be $\dfrac{1}{18}$. We haven't learned integration yet in class so I'm not sure what to do here. Thank you.
Answer
$$f'(a)=\lim_{h\to0}\frac{f(a+h)-f(a)}{h}$$
The question is asking you to identify what the function $f$ is, and what the value of $a$ is that gives you this expression.
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