Question 6I 6. Based on our class discussions, recall that some functions are defined implicitly by a relationbetween z and y such as z² + y² = 25. In such cases, differentiating with respect to z both sideshelps us compute . We should be careful, however, with the Chain Rule that needs to be appliedin the way. That is, if y is assumed to be a function of z, then(1²) = 2y(3')1(VD" = (5(e")' = (e");/and so on.This process is called implicit differentiation.I. Apply implicit differentiation to compute for:z²+ /#j + y° = 19II. Find the equation of the tangent line to the curve z² + VEj +y = 19 at the point (1, 4).Note: Recall that, in general, the slope of the tangent line to f(x) at the point(a, f(a)) is f'(a). In this case, since y is implicitly assumed to be a function of x, theslope of the tangent line becomes y, or , calculated at z= a and y = f(a).7. Now, recall that we have already seen some of the limits discussed below in the previouspractice and midterm exams.You must explain each and every step in order to receive credit. Only when appropriate, i.e.in the cases or , we may also apply L'Hospital's rule, which makes the computation of certainlimits a little bit easier.L'Hospital's rule states thatS(z)a g(2)lim= lim (2)a g'(z)a)lim%3Db)1lim-z-4c)z+4limi z+2d)lim

Name: Question 6I 6. Based on our class discussions, recall that some functi
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Description: Question 6I 6. Based on our class discussions, recall that some functions are defined implicitly by a relationbetween z and y such as z² + y² = 25. In such cases, differentiating with respect to z both sideshelps us compute . We should be careful, ho