Calculus and Vectors

neat and clean handwriting (no cursive)

2a. 3a. E" PFF'F' Each derivative represents the first principles definition for some function fix). State the function. ; _ . 3(x+hj - 3x , _ . {awn}2 -:ic2 ftx) iggnh b. ftx) Eggh ; _ . 4(x+hj3 - 4x3 , _ _ . [x+hj2 -:ic2 f (x) gnuh d. f (x) glam h 5 -5 m r t _ - \"Itr r = - # f (r) 11113;] ,1 f- f (AC) 1111551] h Use the First Principle Method to determine the derivative of fix) = 7 xf. What slope of the tangent at x = 6? Write the equation of the line for the tangent. Use the First Principle Method to determine the derivative of f(x) = (2x 1?. Hint: expand the binomial first. What slope of the tangent at x = 6? Write the equation of the line for the tangent. Use the First Principle Method to determine the derivative of fix) = g. The height ofa soccer ball after it is kicked into the air is given by hit] = -'-'i.Eit2 + 3.5t + 1, where h is the height. in meters, and t is the time, in seconds. Use the First Principle Method to determine the rate of change of the height of the soccer ball at time t. Determine the rate of change of the height of the soccer ball at 0.5 5. When does the ball momentarily stop? What is the height ofthe ball at this time. Write your own equation in the form if = aix h)2 + k. where a, h, and k cannot equal zero (Di. Use the First Principle Method to determine the rate of change. Select a value of x then calculate the slope of the tangent. Write the equation of the of the line of the tangent