Find the function The following limits represent the slope of a curve y=f(x) at the point {a,f(a)} Determine a possible function f and number a, then calculate the limitlim_{xrightarrow2}frac{5cdot x^2-20}{x-2}

Consider the given limit $\underset{x\to 2}{lim}\frac{5\cdot x^2-20}{x-2}$
Note that, $f^{\prime }(a)=\underset{x\to a}{lim}\frac{f(x)-f(a)}{x-a}$
That implies, $f(x)=5x^2$ and $a=2$
Now obtain the limit as follows
$\underset{x\to 2}{lim}\frac{5\cdot x^2-20}{x-2}=\underset{x\to 2}{lim}\frac{5(x^2-4)}{x-2}$
$=\underset{x\to 2}{lim}\frac{5(x^2-2^2)}{x-2}$
$=\underset{x\to 2}{lim}\frac{5(x-2)(x+2)}{(x-2)}$
$=\underset{x\to 2}{lim}5(x+2)$
$=5(2+2)$
$=5\cdot 4$
$=20$
Hence, the value of the given limit is 20.