Question

Find the value of b, b ≥ 0, for which limx->0 {(sqrt(3x+b)-5)/x} exists

Answer 1

\[\lim_{x \rightarrow 0}\frac{\sqrt{3x+b}-5}{x} \cdot \frac{\sqrt{3x+b}+5}{\sqrt{3x+b}+5}\]
\[\lim_{x \rightarrow 0}\frac{(3x+b)-25}{x(\sqrt{3x+b}+5)}\]


so we want the x on top to cancel x on bottom
only way this happens if we let b-25=0 => b=25

Answer 2

\[\lim_{x \rightarrow 0}\frac{3x}{x(\sqrt{3x+25}+5)}=\lim_{x \rightarrow 0}\frac{3}{\sqrt{3x+25}+5}=\frac{3}{\sqrt{3(0)+25}+5}=\frac{3}{10}\]
see limit exists! :)

Answer 3

THANK YOU! :)

Answer 4

np