# How do you find the limit of #(sin (2x)) / (sin (3x)) # as x approaches 0?

2/3

alternative answer

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graph{sin(2x)/sin(3x) [-3.015, 3.142, -0.607, 2.471]}

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To find the limit of (sin (2x)) / (sin (3x)) as x approaches 0, we can use the concept of L'Hôpital's Rule. By applying this rule, we differentiate the numerator and denominator separately and then take the limit as x approaches 0.

Differentiating the numerator, we get 2cos(2x). Differentiating the denominator, we get 3cos(3x).

Taking the limit as x approaches 0, we have: lim(x→0) (2cos(2x)) / (3cos(3x))

Substituting x = 0 into the expression, we get: (2cos(0)) / (3cos(0))

Simplifying further, we have: 2/3

Therefore, the limit of (sin (2x)) / (sin (3x)) as x approaches 0 is 2/3.

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