question_answer

If \[2x+y=1\] is a tangent to \[y=f(x)\] at \[x=\frac{1}{3},\] then \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{\sin x-\sin 3x}{f\left( \frac{{{e}^{3x}}}{3} \right)-f\left( \frac{{{e}^{-3x}}}{3} \right)}\]is equal to _____.

Answer:

0.5