A skydiver jumps out of a plane that is flying 2500 meters above the ground. The skydiver's height, h, in meters, above the ground after t seconds is h(t) = 2500-4.9t. a) Determine the rate of change of the height of the skydiver at t = 5s b) The skydiver's parachute opens at 1000m above the ground. After how many seconds does this happen? c) What is the rate of change of the height of the skydiver at the time found in part b)? 6) Simplify and then differentiate 10x4-6x 2x a) f(x) = b) f(x) = (5x+ 2) 7) A skydiver jumps out of a plane that is flying 2500 meters above the ground. The skydiver's height, h, in meters, above the ground after t seconds is h(t) = 2500 - 4.9t. a) Determine the rate of change of the height of the skydiver at t = 5s 4) Find the derivative of each function a) f(x) = 2x + x d) p(a) = -2a 15 b) y = x5 - 3x e) k(s) = + -754 c) h(t) = -1.1x4 + 78 5)a) Determine the point at which the slope of the tangent to each parabola is zero. i) y = 6x 3x + 4 ii) y -x + 2x + 3 1) Circle the functions that have a derivative of zero: A) y = 8.7 B) y = 4+x c) y = -x 2) For each function, determine a) y = x d) y = x dy dx b) y = x e) y = / D) y = 7 c) y = -3x+ f) y =/ 11 E) y = -7.1 3) Determine the slope of the tangent to the graph of each function at the indicated value. a) y = 6 at x = 12 b) f(x) = 2x5 at x = 3 c) y = = at x = -2 3x 5) Use the graph to determine the following limits a) lim_h(x) x-1+ b) lim h(x) X--1- c) lim_h(x) x--1 d) lim h(x) e) lim h(x) X-3- f) lim h(x) X-3 3 96 34 3 -3 y=h(x) 3 6 48 3) Complete the following table and use results to estimate lim x--1+x+1 4) Use the graph to find the following limits: a) lim b) lim X--1-x+1 c) lim X x-2 x-x-2 X-1x+1 x-2 x-2x-x-2 1.9 1.99 1.999 2.001 2.01 > 6 + N 02 -6 -4 -2,0 2 I T2 2.1 I I +4 1 f(x) 4 42 x+1 6 x 1) Evaluate each limit 3x a) lim- x-2x+2 2) Evaluate the limit of each a) lim 4-x x-2 2-x 16-x X-4x +64 d) lim b) lim (x+x + x) X--1 b) lim 2x +5x+3 X-1 x+1 x-16 x-4x-5x+6 e) lim c) lim (x+1 c) lim x-27 X-3 x-3 x+x X-1 x+1 f) lim