1) (10 pts) How close does the line 4y - 3 = 5x come to the point (-4, -1)? (show all of your work): 2) (15 pts) Evaluate the following limits: (show all of your work): a) lim 2x2 - 3x + 4 b) lim x3+2x2-1 X--2 5-3x c) lim x40 X-+2x-3 dj lim *41 1-+2x-33) (5 pts) If the position of an object with respect to time is shown as a function f (x), then fill in the blanks using only the choices on the right: a) Snap= f (x) b) Acceleration = f' (x) c) Velocity = f" (x) d) Jolt = for ( x ) e) Position - for (x) 4) (15 pts) For f(x) = 2x- - 4x + 1, perform the following: (show all of your work) a) Find [(xth)-f(x) b) Find lim [x+h)-f(x] h-+0 (r+h)-x c) Evaluate your answer to part b) at x = 2 d) Find an equation of the line tangent to the graph of f(x) at (2, f (2))5) (10 pts) For f(x) = 7x3 + x, perform the following: (show all of your work) a) Find f'(x) b) Find f'(3) 6) (15 pts) Find f'(x) for the following: (show all of your work) a) f( x)=xte* b) f (x) = V4x* +x c) f (x) = sins(x)7) (15 pts) An object of mass m is attached to a spring and has a height of h(t) = 3 + sin(t) feet at time t seconds. Answer the following and show all of your work. a) Find the height and kinetic energy of the object when: i. t = 1 sec ii. t = 2 sec ili. t = 3 sec b) Find the rate of change in the kinetic energy when: i. ii. t = 2 sec iii. t = 3 sec c) Why is this an unrealistic model of the motion of a mass attached to a real spring?8) (15 pts) Find values for the coefficients a, b and c so that the parabola f (x) = ax + bx + c goes through the point (0, 1) and is tangent to the line y = 3x - 2 at the point (2, 4). Show all of your work