770. 1) lim _(xarrow 0)(arctgx)/(x) y k a 3 a HHe. Ilo.JozKHT (1-2x)-alpha

To find the limit of the, we can use L'Hopital's rule. L'Hopital's rule states that if the limit of a function is in the form of 0/0 or ∞/∞, we can differentiate the numerator and denominator separately and then take the limit again.In this case, the given expression is . As x approaches 0, both the numerator and denominator approach 0, so we can apply L'Hopital's rule.Differentiating the numerator with respect to x, we get . Differentiating the denominator with respect to x, we get 1.Now, we can take the limit of the expression as x approaches 0.Substituting x = 0 into the expression, we get .Therefore, the limit of the given expression is 1.