Question

a ball falls from a height of 5m on the horizontal plane if the coefficient of restitution is 0.4

Answer 1

Answer:

yes your answer is correct 0.4

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Answer 2

$\tt \fcolorbox{skyblue}{skyblue}{This \: is \: the \: answer \: of \: your \: previous \: question}$

SOLUTION :

$\sf \lim_{x \to \: 0}\frac{1 - \cos(2 {x}^{3} )}{x \: { \sin}^{2}2x { \tan}^{3} 3x } \\ \\ \implies \: \sf\lim_{x \to \: 0} \frac{ \frac{1 - \cos 2 {x}^{3} }{( {2 {x}^{3}) }^{2} } }{ \frac{ { \sin}^{2} 2x}{ {(2x)}^{2} } \times \frac{x \: { \tan}^{3}3x }{ {x}^{4} } } \\ \\ \sf \: putting \: limiting \: value \: \\ \\ \implies \: \sf \boxed{ \mathfrak{ \frac{1}{2} }}$

REQUIRED FORMULAS :

$\sf 1. \lim_{x \to \: 0} \frac{ \sin \: x}{x} = 1$

$\\ \sf \: 2. \lim_{x \to \: 0} \frac{1 - \cos \: x}{ {x}^{2} } = \frac{1}{2}$

$\sf \: 3. \lim_{x \to \: 0} \frac{ \tan \: x}{x} = 1$

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