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Maths-

General

Easy

Question

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 3 sin space x minus sin space 3 x over denominator x cubed end fraction$

0
1
${(\frac{π}{180})}^{3}$
$4 {(\frac{π}{180})}^{3}$

The correct answer is: $4 open parentheses pi over 180 close parentheses cubed$

$limit as x rightwards arrow 0 of open parentheses fraction numerator 3 sin x minus sin 3 x over denominator x cubed end fraction close parentheses equals limit as x rightwards arrow 0 of open parentheses fraction numerator 4 sin cubed x over denominator x cubed end fraction close parentheses equals open parentheses straight pi over 180 close parentheses cubed limit as x rightwards arrow 0 of open parentheses fraction numerator 4 sin cubed open parentheses begin display style straight pi over 180 x end style close parentheses over denominator x cubed open parentheses straight pi over 180 close parentheses cubed end fraction close parentheses equals open parentheses straight pi over 180 close parentheses cubed limit as x rightwards arrow 0 of 4 open parentheses fraction numerator sin open parentheses begin display style straight pi over 180 end style x close parentheses over denominator open parentheses straight pi over 180 x close parentheses end fraction close parentheses cubed equals open parentheses straight pi over 180 close parentheses cubed cross times 4 cross times 1 equals 4 open parentheses straight pi over 180 close parentheses cubed$

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