MATLAB

The functions

f(x)= (sqrt(x^2+1) - 1) /x^2 and g(x) = 1/ (sqrt(x^2+1) +1)

1)Using MATLAB compute the limit as x approaches to 0 by looking at the values x=1/2^i for i=1:30

2) What happens if you set r=sqrt(ulp) and evaluate f(r) and g(r)?

anything would help.

Quote:

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Originally Posted by Juancd08

The functions

f(x)= (sqrt(x^2+1) - 1) /x^2 and g(x) = 1/ (sqrt(x^2+1) +1)

1)Using MATLAB compute the limit as x approaches to 0 by looking at the values x=1/2^i for i=1:30

2) What happens if you set r=sqrt(ulp) and evaluate f(r) and g(r)?

anything would help.

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First it would help if you created function for the functions.

something like:

Code:

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function rv=ff(x)
  rv=(sqrt(x.^2+1)-1)./x.^2;

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and:

Code:

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function rv=gg(x)
  r=1./ (sqrt(x.^2+1) +1);

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then:

Code:

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i=1:30;
x=2.^(-i);
 
ff(x)
gg(x)

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Will show the values at a sequence of points approaching zero.


RonL