We want to determine
[tex]lim_{x\rightarrow16}\, \frac{5\sqrt{x}-20}{x-16} [/tex]
Note that
x-16 = (√x + 4)(√x - 4)
Therefore
[tex]lim_{x\rightarrow16}\, \frac{5\sqrt{x}-20}{x-16} \\=lim_{x\rightarrow 16} \,\frac{5(\sqrt{x}-4)}{(\sqrt{x}+4)(\sqrt{x}-4)} \\=lim_{x\rightarrow 16}\, \frac{5}{\sqrt{x}+4}\\= \frac{5}{\sqrt{16}+4} \\= \frac{5}{8} [/tex]
A graph of the function verifies that the solution is correct.
Answer: [tex] \frac{5}{8} [/tex]
