Solution to Midterm exam Fall 2010--a

# Solution to Midterm exam Fall 2010--a - EGM 3344...

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EGM 3344 Introduction to Numerical Methods of Engineering Analysis Midterm Exam Fall 2010 Name: , Grade: Closed book; 1 page formula sheet (8.5″ x 11″). Only scientific calculator is allowed. 1a. (6 points) The true value of x T =0.061838367… was approximated by John as x A =0.0 618 3. How many significant digits does his x A have based on the given x T ? Solution: # of significant digits = 3 1b. (6 points) For f ( x )= x 3 +e 2( x-1) , the Taylor series expansion near x =1 in the form of f ( x )= a 0 + a 1 ( x -1) + a 2 ( x -1) 2 + a 3 ( x -1) 3 + … is needed. What are the values of a 0 , a 1 , and a 2 ? Solution: f(1)=1+1=2, f (1)=3+2=5, f =6+4=10 f(x)~2+5(x-1)+5(x-1) 2 +… a 0 =2, a 1 =5 and a 2 =5. 1c. (6 points) A student wrote the following function: function result=myfun(a) reciprocal=1/a; result=2*reciprocal In the Matlab command window, the student typed the following: >>clear >>a=3 >>myfun(a) >>reciprocal What value do you expect Matlab to print for reciprocal , and why? Solution: Matlat will give: “ ??? Undefined function or variable 'reciprocal' . ” Basically, you should not get any meaningful value for 'reciprocal' since it is only defined INSIDE the function and it not exported to the workspace.

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