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Question Number 141509 by I want to learn more last updated on 19/May/21

\lim_{θ \to 0} \frac{\sin^{3} 3 θ - 3 θ^{3}}{θ^{3} + θ^{4}}

Answered by bramlexs22 last updated on 20/May/21

\lim_{θ \to 0} \frac{27 θ^{3} - 3 θ^{3}}{θ^{3} (1 + θ)} = \lim_{θ \to 0} \frac{24 θ^{3}}{θ^{3} (1 + θ)} = 24

Commented by I want to learn more last updated on 20/May/21

Thanks sir . I appreciate . How did the \sin turn to 27 θ^{3} sir

Commented by physicstutes last updated on 20/May/21

for small angles that is θ \to 0, \sin θ \to θ

so \sin^{3} 3 θ = {(\sin 3 θ)}^{3} \to {(3 θ)}^{3} = 27 θ^{3}

Commented by I want to learn more last updated on 20/May/21

Thanks sir . I appreciate .