Question

Use a table of values to estimate the value of the limit. Confirm your result graphically by graphing the function with a graphing device. . If the limit does not exist enter DNE. . . \lim_{x\to 0} \frac{\sqrt{x+25}- 5}{x}

Answer 1

Hello,

$\lim_{x \to 0}\dfrac{ \sqrt{x+25}-5}{x}$

$=\lim_{x \to 0}\dfrac{(\sqrt{x+25}-5)*(\sqrt{x+25}+5)}{x*(\sqrt{x+25}+5)}$

$=\lim_{x \to 0}\dfrac{x+25-25)}{x*(\sqrt{x+25}+5)}$


$=\dfrac{1}{10}$