lim (4x' + 5x - 12) 5. a. Evaluate x-+2 b. What is the meaning of this value? 6. Evaluate the following limits. x- - 16 a. lim x-4 x - 4 b. 8x3 - 5x2 + 17 lim X-+00 6x3 + 2x2 - 4x 49 + h - 7 C. lim h-0 h y - 8 . lim y-2 2y2 - 10y + 12 e. 2th - 2 lim h-0 h 7. Find the slope of the tangent line at point (-1,2) on the curve f(x) = 5x 2+ 2x using First Principles. 8. Find the derivative of the function f (x) = x2- 10x + 3 using First Principles. 9. Using first principles, determine the equation of the tangent line at point (-1, 13) on the curve f(x) = x2 - 5x + 7. 10. At what point on the parabola y = 3x 2 + 2x is the tangent line parallel to the line y = 10x - 2? Use first principles in your solution.'l . Determine the average rate of chance of v in the function v= 4x 3 - x 2 + 2x - 3 over the interval [1.3]. 2. Given the function x} = 2x2 + 4x+ 1 a. Use the secant method to nd the instantaneous rate of change when x = 1. b. Use First Principles to find the value of the derivative when x = 1. c. What did 1you notice? 3. Explain the difference between a secant line and a tangent line. How do they.' relate to the rate of change ofa function? Include a sketch of each type of line in your solution. 4. The path of a baseball relative to the ground can be modelled by the function d} = f1 + 'l'lt + 1. where dit} represents the height of the ball in metres. and t represents time in seconds. a. Find the average rate of change of the ball between 1 and 3 seconds. b. Using the secant method. nd the instantaneous rate of change at 2 seconds