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Evgen [1.6K]
2 years ago
9

a1" title="\lim_{x \to 0 } \frac{x-sin(2x)}{x+sin(3x)}" alt="\lim_{x \to 0 } \frac{x-sin(2x)}{x+sin(3x)}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
nekit [7.7K]2 years ago
5 0

Step-by-step explanation:

=  \lim \limits_{x \to0} \frac{x -  \sin(2x) }{x +  \sin(3x) }

=  \lim \limits_{x \to0} \frac{ \frac{d}{dx}(x -  \sin(2x) ) }{ \frac{d}{dx} (x +  \sin(3x) )}

=  \lim \limits_{x \to0} \frac{1 -  2\cos(2x) }{1 + 3 \cos(3x) }

=  \lim \limits_{x \to0} \frac{ \frac{d}{dx}(1 + 2 \cos(2x) ) }{ \frac{d}{dx} (1 + 3 \cos(3x) )}

=  \lim \limits_{x \to0} \frac{ - 4 \sin(2x) }{ - 9 \sin(3x) }

=  \frac{ - 4.2}{ - 9.3}

=  \frac{ - 8}{ - 27}

=  \frac{8}{27}

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