help with these questions.

1. Evaluate the following limits. at) lim 2 3x2 x~>71 b) lim ex x~>4m 2. Determine the derivatives of the following functions. Do Not simplify your answers. a) y:(1+w/m)S 1lnx b : ) y (3x2 5)7 c) y = (sin x)6 (62*) 3. Are the following quantities Scalars (S), Vectors (V) or Meaningless (M)? a) 100 Nm of Torque is being applied down into the screw. b) a-(bxc) C) b 7 b 4. Vectors a and b, with {al = 13 and |b| = 7, a is horizontal and b is 600 above a. a) |a + bl b) The direction of [a + b| relative to a 0) 30b Page 1 of 11 Name: 5. List Given vectors a = [1, -2, 3] and b : 3i i 2]; determine the following. w aOb b) 13 c) the angle between a and b d) a vector orthogonal to both a and b Z e) Sketch vector b 6. Given the graph of f I, determine the following intervals: a) the graph of f is decreasing b) the graph of f is concave down 7. a) What is the magnitude of torque produced when a 300 N force is applied at an angle of 270 to a wrench that is 20 cm long? b) What is the direction of the torque? Page 2 of 11 Name: Part-C Communication 8. A function, f, has all the properties listed below. Sketch the graph of y =f(x). a) x) is an odd function, f(x) has no yintercept b) lim f(x) = 2, x~>+uc c) f(3) = 5, f'(3) = 0, M3) 0 for x > 6 9. A motorist driving on a straight and level road approaches an intersection. He sees a stop sign and applies his brakes. His caI slows down in a way that his velocity, in z meters per second, after t seconds is m) = 807101;. :1) Determine the initial velocity of the car. b) How long does it take the car to stop? c) Determine the acceleration function of the car. e) Calculate the average acceleration of the car while braking. Page 3 of 11 Name: 10. Provide a sketch of a function f(x) that is discontinuous at x = 3 because. .. a) f(3) does not exist b) lim f (x) # f(3) X->3 11. Determine the following limits exactly if they exist, and state if they do not. x3 - 8 a) lim- x-2 2x- + x-10 b) lim- 9x4 - 3x7 + 6 x-700 2x - x4+6x c) lim 5x - x2 x -$ 5- Jx - 51 d) lim (1 + x) lim ( xth ) 12 - x12 e) h - h f) Given the graph of f(x), evaluate lim f (x) 2 - x *>0 g) Given f (x) = Vx + 4 x = 0, evaluate lim f (x) x 2 + 2 x