Answer to Quiz 11 Fri 20 Apr 2007

1. The central difference approximation for the derivative of a function f at x is defined by the formula y = (f(x+h) - f(x-h))/(2h), for h > 0.
   1. Write a MATLAB function centdiff which takes on input f, x, and h, and which returns in y the central difference approximation for f'(x). Complete

      function y = centdiff(f,x,h)
      %
      %  The function y = centdiff(f,x,h) returns the central difference
      %  approximation for the derivative of f at x, using step size h.
      %
      

   2. Give the MATLAB command to use centdiff to approximate the derivative of sin(x) for x = 1.3 using h = 0.01. Give the value returned by your centdiff.

   Answer:

   1. the completion of the function:

               y = ( feval(f,x+h) - feval(f,x-h) ) / ( 2*h );
      

   2. the function call and its value:

               centdiff('sin',1.3,0.01)
      	                             0.2675
      

2. Give all MATLAB commands to make a surface of revolution, around the vertical axis. Revolute r = exp(t) for t in [0,1] around the vertical axis.
   Sketch the surface you obtain.

   Answer:

                   t = 0:0.01:1;
                   r = exp(t);
                   cylinder(t);
   
   % see the paper handout for the sketch...