# How do you find the limit of #(arctan(x)) / (5x)# as x approaches 0?

By applying L'Hospital's rule, we take the derivative of the numerator and denominator, giving us

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A lengthier approach using trig is explained below.

Just in case you're not comfortable with L'Hopital's Rule, or have not yet been exposed to it, another approach to solving the problem involves using the definition of the arctangent function.

Recall that if

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To find the limit of (arctan(x)) / (5x) as x approaches 0, we can use L'Hôpital's rule. Taking the derivative of both the numerator and denominator, we get 1 / (1 + x^2) / 5. Substituting x = 0 into this expression, we find that the limit is 1 / 5.

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