Question

$$lim_{x\rightarrow0}(\frac{x^{2}+\sin\ 3x}{2x-\sin\ x})$$

Answer

l<0

Solution


Remove parentheses.
\[l\imath mx->0\times \frac{{x}^{2}+\sin{3x}}{2x-\sin{x}}\]
Simplify  \(0\times \frac{{x}^{2}+\sin{3x}}{2x-\sin{x}}\)  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 \(-1\).
\[l<0\]