Given below are two statements:
Statement I: The conversion proceeds well in a less polar medium. \[ {CH}_3{CH}_2{CH}_2{CH}_2{Cl} \xrightarrow{{HO}^-} {CH}_3{CH}_2{CH}_2{CH}_2{OH} + {Cl}^- \] Statement II: The conversion proceeds well in a more polar medium. \[ {CH}_3{CH}_2{CH}_2{CH}_2{Cl} \xrightarrow{{R}_3{N}} {CH}_3{CH}_2{CH}_2{CH}_2{NH}_2 + {Cl}^- \] In the light of the above statements, choose the correct answer from the options given below:
Both statement I and statement II are true
To evaluate the given statements about organic reactions involving conversion of \({CH}_3{CH}_2{CH}_2{CH}_2{Cl}\), let's examine each one:
After understanding both reactions, we can conclude that:
Let \( f : \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \[ (\sin x \cos y)(f(2x + 2y) - f(2x - 2y)) = (\cos x \sin y)(f(2x + 2y) + f(2x - 2y)), \] for all \( x, y \in \mathbb{R}. \)
If \( f'(0) = \frac{1}{2} \), then the value of \( 24f''\left( \frac{5\pi}{3} \right) \) is: