Math 155-004, Quiz 11
April 21, 2009
NAME:
Instructions: This quiz is closed books and closed notes. You may use calculators. Work that is erased or
crossed out will not be graded.
1. (3 points) Use the tangent line approximation with base point a = 3 to estimate 3.032 .
2. (3 points) Consider the process of using Newton’s Method to find an equilibrium of pt+1 = pt −p2t +sin(pt ).
(a) Write Newton’s Method as a discrete-time dynamical system for this example; use xt+1 and xt .
(b) Find x1 if x0 = 1.
3. (4 pts) Use Euler’s Method to approximate y(1) if
dy
dt
= t2 and y(0) = 2. Use ∆t = 0.5.
Extra Credit: Topology is the mathematical study of shapes. Circle the two of the following that are
topologically equivalent:
trefoil knot
coffee mug
doughnut
sphere