1) Consider the following data set: [K] _I__ __ Calculate average rate of change in y over each interval (part a and b). Determine an approximation for the instantaneous rate of change in y at x = 1(part c) a)3Sxl b)lx5 c} x = l 2)Which of the following statements is truet' false? {TI F) [K] a) Discontinous functions are non- differentiable at the points where they are discontious b} If the derivative does not exsit at a point on the curve, the function could be differentiable at that x-valuc c} The limit of the function at x =a maybe exist eventhOugh the function is diScounteOUS at x = a d} The instantaneous rate of change refers to the rate of change ofa function over an interval e} The derivative of y=f {x} is a new function y= f '(x), which represents the slope of the secent line at any point on the curve ofy= f (x) 3) Evaluate each limit for the graph. lim f(x)= lim f(x)= lim f(x)= * 3+ 4) Calculate the following limits. [T] a) lim * +5x+6 x-3 X-3 b) lim *-9 VX - 3 -95) Determine the derivative of f (x) = x2 + 2x using first principles definition of the derivative. [K] 6) Calculate derivative of following functions with respect to x. [T] a) f(x) = x5 +0.5 x4 - 2x2 - 5x + 3 b) f (x ) = (x2 + 1)(3x -3) c) f(x) = *+3 Vx2-1d) = - +- e)f (x) = 2Vx - 3Vx f) f(x) = 8x2 x2-9 g) s(t) = = +3 - 5+27) Assume that height of the rocket at time t can be modelled by the function h(t) = -4.9 t2 + 34.5 t + 3.2 [ a) Determine functions that represents the velocity and the acceleration of the rocket b) Calculate the height, the velocity and the acceleration of the rocket at t = Is. 8) Determine the second derivative of the following function at x = 1. [T] a) f(x) = x3 - 3x2 + 7x - 9 b) f ( x ) = (x2 - 1) (x3 + 7)