Using the derivative rules, please show that: d + dx In [f (x) g(x) ] ) = f'(x ) g'(x) f (x) g(x) Source: Rogawski Ed. 2Please use logarithmic differentiation to find derivatives of the following functions. Final Answer e"cos' x V = x'+x+1 Final Answer v = vx e(x-x) (1-x) 2/3Q #6 - Q #9 For the function f (x) shown below, please complete this table for a = 1, 3, 5, 6. If the value exists, please state it. If not, please enter DNE. Q.#6 Q.#7 Q.#8 Q.#9 a =1 a=3 a = 5 a = 6 lim f(x) x- a lim f(x) x- a 2 lim f(x) 2 3 4 56 f (a)Q #10 Q.#15 For the function f (x) shown below, please complete this table for a: - 0c, -2 ,-1_._ 2, + 30 . If the value exists, please state it. If not, please enter DNE. Q #16 Please evaluate Lim in three ways: X-> -00 a) numerically using sample values to estimate the limit Hint: Use progressively larger negative x-values. b) graphically by sketching its graph to find the limit exactly c) algebraically to find limit exactly Hint: Direct substitutionQ.# 17 - Q.#19 Please use f (x) given below to answer questions. x+2 for x 2 Q.#17 - Q.#18 Please complete this table by finding the values algebraically using f(x) as given. If the value exists, please state it. If not, please enter DNE. Q. #17 Q. #18 a = - 1 a = 2 Lim f(x) * - a - Lim f(x) x -> at Lim f(x) x - a fla) Final Answer Q.#19 Please sketch the graph of f(x) and use it to check values in table. Just see graph at left !