Using the given table, evaluate the expression. You may assume that f(x) and g(x) are c functions. C 2 4 5 8 11 14 f (ac) -11 13 2 9 17 g(x) -13 -14 17 -17 -16 -15 f' (z) -14 19 -4 -15 -5 18 g (x) -12 4 7 5 8 -10 A. d'(5), where d(x) - xf(x). d' (5) B. p'(8), where p(x) - 9(f(x)). p'(8) = C. c'(11), where c(x) - f(x). c' (11) = D. lim f(x) . g(x) 1 4 2 - 16 f(x) . 9(x) The limit exists, lim x - 4 2 - 16 The limit does not exist.A particle moves on a horizontal line so that its position, in centimeters, at time t, in seconds, is giver s(t) = to - 16.5t + 54t - 7, with t > 0. Assuming that the positive direction is to the right: A. Determine the velocity function, v(t) . v (t) = Evaluate v(5) . v (5 = Interpret, with a complete sentence and appropriate units, the meaning of v(5) and its value. B. Determine the t -interval(s) when the particle is moving to the right.Consider the function f (ac) - 2x - 4 sin x on the domain [0, 27]. Use analytic techniques (calculus, algebra, trigonometry) to determine the intervals where the function is increasing and decreasing. Use exact values in your response. f (z) is increasing on f (x) is decreasing onThe top of a 21 foot long ladder is sliding upward at 2.4 feet per second along a vertical wall. The base of the ladder is on the horizontal ground. At the moment that the top of the ladder is 11 feet from ground level: a) How far from the bottom of the wall is the base of the ladder? feet b) The base of the ladder is moving |Select an answer v the wall at feet per second.The Geteway Arch, in St. Louis Missouri, is approximately 192 meters tall. A camera is 50 meters from the base of the arch and is moving along the horizontal ground away from the arch while keeping the top of the arch in view. What is the camera's horizontal velocity when the angle of elevation (to the top of the arch) is decreasing at 0.06 radians per second? m s You may round your final response to two decimal places.Use differentials or a linear approximation to approximate 3 727. Hint: 727 is close to 729. 3/727 ~ You may round your final response to four decimal places