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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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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