MATH 160

FINAL EXAM

 

  1. (24 pt) Find the following limits:

    2. a) b) c) d)

    e) f)

     

  2. (5 pt) Use the definition of the derivative to find the derivative of .
  3. (20 pt) Find the derivative for the following functions

    4. a) b) c) d)

  4. (8 pt) A particle takes off from the ground (s(0)=0) and has initial velocity 1 (v(0)=1). Its acceleration is given by a(t)=cos(t) for t ³ 0. Find the position function of the particle for t ³ 0 and sketch it.
  5. (5 pt) Use either differentials or Newton’s Method to estimate .
  6. (6 pt) Find the maximum and minimum values of the function on the interval [-1,2].
  7. (10 pt) A plane flies at a constant height of 3 miles above the ground at velocity of 200 mi/hr. The flight path takes the plane directly over a radar station on the ground. How fast is the distance between the plane and the station changing when the plane is 5 miles from the station?
  8. (6 pt) Use the definition of the definite integral to evaluate . Use the Fundamental Theorem of Calculus to check your answer.
  9. (10 pt) Sketch the function . Make note of local max/min values, points of inflection, and asymptotes.
  10. (6 pt) Use implicit differentiation to find the tangent line to at the point (-1,2).
  11. (Bonus 5pt) Show that among all rectangles of fixed area A, a square has the smallest perimeter.
  12. (Bonus 5pt) The picture of the following function. Where is the function continuous? Where is it differentiable? Sketch the derivative.