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

Use

I like the first method (above) Here's a second method.

So

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To evaluate the limit of sin(3x)/x as x approaches 0, we can use the concept of L'Hôpital's Rule. By applying this rule, we differentiate both the numerator and denominator with respect to x. The derivative of sin(3x) is 3cos(3x), and the derivative of x is 1.

Taking the limit of the differentiated function, we have 3cos(3x)/1, which simplifies to 3cos(0) = 3.

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

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