# How do you find the limit of #(1-cos(4x))/(1-cos(3x)# as x approaches 0?

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To find the limit of (1-cos(4x))/(1-cos(3x)) as x approaches 0, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get (-4sin(4x)) / (-3sin(3x)). Evaluating this expression as x approaches 0, we have (-4sin(0)) / (-3sin(0)), which simplifies to 0/0. Applying L'Hôpital's Rule again, we differentiate the numerator and denominator once more. This gives (-16cos(4x)) / (-9cos(3x)). Substituting x=0, we have (-16cos(0)) / (-9cos(0)), which simplifies to -16/-9. Therefore, the limit of (1-cos(4x))/(1-cos(3x)) as x approaches 0 is 16/9.

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