Question

the formula $lim_{h
ightarrow0}\frac{h^{2}-0}{h}$ represents $f^{prime}(a)$ for some function $f$ and some number $a$. find $f(x)$ and $a$. $f(x)=square$ $a = square$

Explanation:

Step1: Recall the definition of the derivative

The definition of the derivative $f^{\prime}(a)=\lim_{h
ightarrow0}\frac{f(a + h)-f(a)}{h}$.

Step2: Compare with the given limit

We have $\lim_{h
ightarrow0}\frac{h^{2}-0}{h}=\lim_{h
ightarrow0}\frac{(0 + h)^{2}-0^{2}}{h}$. Comparing with $\lim_{h
ightarrow0}\frac{f(a + h)-f(a)}{h}$, we can see that $f(x)=x^{2}$ and $a = 0$.

Answer:

$f(x)=x^{2}$
$a = 0$