3. Given that lim _(xarrow 0)(f(x))/(Ax^4)+Bx^(2)=C find lim _(xarrow 0)(f(x))/(x^2) 20p

To find the limit of the given expression, we can use the fact that the limit of a quotient is equal to the quotient of the limits, provided that the limit of the denominator is not zero.Given that , we can rewrite this as: Since the limit of as approaches 0 is 0, the first term becomes 0. Therefore, we have: Now, we can use the fact that the limit of a quotient is equal to the quotient of the limits: Since the limit of as approaches 0 is 0, we have: This is an indeterminate form, and we need to use L'Hopital's rule to evaluate it. L'Hopital's rule states that if the limit of a quotient is in the form or , then the limit of the quotient is equal to the limit of the quotient of their derivatives.Differentiating the numerator and denominator with respect to , we get: Evaluating the limit of this expression as approaches 0, we get: This is still an indeterminate form, and we need to use L'Hopital's rule again. Differentiating the numerator and denominator with respect to , we get: Evaluating the limit of this expression as approaches 0, we get: Therefore, the limit of the given expression is .