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- Homework Statement
- We are required to explain the values of g(x) and h(x).

The script for Matlab is:

g = @(x) (exp(x)-1-x)./x.^2;

h = @(x) (exp(x)-x-1)./x.^2;

x = 1e-10;

fprintf(’x=%.16e\ng(x)=%.16e\nh(x)=%.16e\n’, x, g(x), h(x))

x = 2^(-33);

fprintf(’x=%.16e\ng(x)=%.16e\nh(x)=%.16e\n’, x, g(x), h(x))

The output is:

x=1.0000000000000000e-10

g(x)=8.2740370962658164e+02

h(x)=0.0000000000000000e+00

x=1.1641532182693481e-10

g(x)=0.0000000000000000e+00

h(x)=0.0000000000000000e+00

- Relevant Equations
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I am having a bit of trouble understanding what the values of g(x) and h(x) mean. I went through it by hand and here is information that I gathered about the values and questions I am trying to answer to gain a better understanding. Firstly, for the value of x=1e-10 both the numerator of g(x) and the numerator of h(x) equate to the same number on my calculator and of course they have the same denominator, but then I don't understand why g(x) equals a positive number whereas h(x) equals 0, does this all just come from the error? I get the answer I am expecting for g(x) but not h(x).

Secondly, when I calculate g(x) for x=2

Any help would be appreciated, thanks.

Secondly, when I calculate g(x) for x=2

^{-33}I get a negative number and when I calculate h(x) when x=2^{-33}I get 0. But why would the output for g(x) be 0 on MATLAB but when I calculate it I obtain a negative number? Is this simply only due to the precision of using 16 decimals whereas on my calculator it's much less?Any help would be appreciated, thanks.