- Question 1 Let y = 272-3x.343_512 72r+3 a) Given that In (y) can be written in the form In (y) - In (A) 23 + In (B) 12 + In (C) z+ In (D). What are the coefficients A, B, C, and D ? A = B= C = D = b) Using the correct answer to (a), and implicit differentiation, find the value of when I = 0. Answer: - Question 2 Find the equation of the tangent line to the curve y = 5In (23 ex4) at the point (1, 5) . (Hint: simplify before differentiating.) Your answer must be an equation of the form y = mr + b. This question accepts equations. E.g. y-2 = 5(x-4)+1. - Question 3 If f (z) - In (2x +1) , then its fourth derivative is f (4) (z) =- Question 4 Evaluate lim In (2 + h) - In (2) h-+0 h - Question 5 Consider the function f(x) = 3arcsin(x) arccos(r) - 6arctan(I). What is the derivative of f(x) at z = 07 Answer: f' (0) = FORMATTING: Your answer should be exact. Remember to write symbols like w and vi as pi and sqrt(x), respectively.Question 7 Consider the function f(x) = (arctan(z))# + 3arctan(x) + 3. What is the derivative of f(z)? FORMATTING: In Mobius, arctan() is written arctan(x) Answer. f (z) = Question 9 Consider the equation 3+3-3ry +1. a) Use implicit differentiation to find the derivative of y with respect to a . Your answer will be a function of both a and y . dy b) Now find the equation of the tangent line to the curve described by ro ty - 3xy + 1 at the point (0, 1) - Answer. FORMATTING: Your answer must be in the form of an equation for y in terms of a; e.g. y = ax + b.- Question 6 Match the following numbered functions with their derivatives: v d sec(I) d CSC(I) tan(I) d cot(I) darcsin(I) d arccos(I) di - v arctan(I) 1. sec (I) 2. 1+72 3. V1-22 4. - cot(I) CSC(I) 5. tan(I) sec(I) 7. - csc-(I)