Composition of Functions and Sequence
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1.2 I tried to sort it but obviously something is wrong...
syms x y
f = 1/(x+1); h = exp(x); g = 1;
h = compose(f,g)
1.3 I have no idea whats it is about.
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rifat
le 1 Sep 2013
Modifié(e) : rifat
le 1 Sep 2013
1.2 - Try to use finverse
1.3 - Use loops to solve
N=3; % number of terms
v=sqrt(2);
for i=1:N-1
v=sqrt(2+v);
end
v
To find convergence use a very large value of N
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Roger Stafford
le 1 Sep 2013
It is more elegant to use the equation given to you by Matt J:
L=sqrt(2+L)
and solve for L. It is the value for which there is no change in the iteration and it is also the value your sequence converges to. You don't need to carry out the iteration for large N to find it, though if you do, you will see that these answers agree.
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Roger Stafford
le 1 Sep 2013
Modifié(e) : Roger Stafford
le 1 Sep 2013
For problem 1.2 I strongly recommend reading up on the definition of function composition. For example:
http://en.wikipedia.org/wiki/Function_composition
You are looking to define a function y = g(x) which has the property that
f(g(x)) = f(y) = h(x) = exp(x)
where f(y) = 1/(y+1). It's easy to solve for y = g(x) in this equation. Then set x equal to 1.
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