Question

$$lim_{x\rightarrow0}\frac{\sqrt{2x+8^{2}}-8}{x}$$

Answer

l<0

Solution


Simplify  \({8}^{2}\)  to  \(64\).
\[l\imath mx->0\times \frac{\sqrt{2x+64}-8}{x}\]
Factor out the common term \(2\).
\[l\imath mx->0\times \frac{\sqrt{2(x+32)}-8}{x}\]
Simplify  \(0\times \frac{\sqrt{2(x+32)}-8}{x}\)  to  \(0\).
\[l\imath mx->0\]
Regroup terms.
\[-+l\imath mx>0\]
Divide both sides by \(\imath \).
\[-+lmx>0\]
Divide both sides by \(m\).
\[-+lx>0\]
Divide both sides by \(x\).
\[-+l>0\]
Multiply both sides by \(-1\).
\[l<0\]