Question

In: Advanced Math

Perform four iterations, if possible, on each of the functions g defined in Exercise 1. Let...

Perform four iterations, if possible, on each of the functions g defined in Exercise 1. Let Po=1 and P(n+1)=g(Pn), for n=0,1,2,3.

b. Which function do you think gives the best approximation to the solution?

heres the functions g defined in exercise 1.

g1(x)=(3+x-2x^2)^1/4

g2(x)=(x+3-x^4/2)^1/2

g3(x)=(x+3/x^2+2)^1/2

g4(x)=3x^4+2x^2+3/4x^3+4x-1

Solutions

Expert Solution


Related Solutions

Let f : N → N and g : N → N be the functions defined...
Let f : N → N and g : N → N be the functions defined as ∀k ∈ N f(k) = 2k and g(k) = (k/2 if k is even, (k + 1) /2 if k is odd). (1) Are the functions f and g injective? surjective? bijective? Justify your answers. (2) Give the expressions of the functions g ◦ f and f ◦ g? (3) Are the functions g ◦ f and f ◦ g injective? surjective? bijective?...
Prove the following: Let f and g be real-valued functions defined on (a, infinity). Suppose that...
Prove the following: Let f and g be real-valued functions defined on (a, infinity). Suppose that lim{x to infinity} f(x) = L and lim{x to infinity} g(x) = M, where L and M are real. Then lim{x to infinity} (fg)(x) = LM. You must use the following definition: L is the limit of f, and we write that lim{x to infinity} f(x) = L provided that for each epsilon > 0 there exists a real number N > a such...
List four functions banks perform. Give a detailed response for each function
List four functions banks perform. Give a detailed response for each function
Let G be a Group. The center of, denoted by Z(G), is defined to be the...
Let G be a Group. The center of, denoted by Z(G), is defined to be the set of all elements of G that with every element of G. Symbolically, we have Z(G) = {x in G | ax=xa for all a in G}. (a) Prove that Z(G) is a subgroup of G. (b) Prove that Z(G) is an Abelian group.
Let g be the function defined by g(x) = x(x + 1). Find g(x + h)...
Let g be the function defined by g(x) = x(x + 1). Find g(x + h) − g(x − h).
Let⇀F and⇀G be vector fields defined on R3 whose component functions have continuous partial derivatives. Furthermore,...
Let⇀F and⇀G be vector fields defined on R3 whose component functions have continuous partial derivatives. Furthermore, assume that ⇀∇×⇀F=⇀∇×⇀G.Show that there is a scalar function f such that ⇀G=⇀F+⇀∇f.
Utility function over clothing (C) and greens (G) is defined by the function U(C,G)=C^(1/4)+G^(1/4). Let P(of...
Utility function over clothing (C) and greens (G) is defined by the function U(C,G)=C^(1/4)+G^(1/4). Let P(of C) and P(of G) denote the prices of cherries and grapes respectively. W is income that is available to consumer to spend on those two goods. (a) Write down the customer's utility maximization problem. (b) set up the langrangian and solve for the first order condition. (c) Solve for the consumer's demand functions for clothing and greens. Please Explain.
In this question we study the recursively defined functions f, g and h given by the...
In this question we study the recursively defined functions f, g and h given by the following defining equations f(0) = −1 base case 0, f(1) = 0 base case 1, and f(n) = n · f(n − 1) + f(n − 2)^2 recursive case for n ≥ 2. and g(0, m, r, k) = m base case 0, and g(n, m, r, k) = g(n − 1, r,(k + 2)r + m^2 , k + 1) recursive case for...
In this question we study the recursively defined functions f, g and h given by the...
In this question we study the recursively defined functions f, g and h given by the following defining equations f(0) = −1 base case 0, f(1) = 0 base case 1, and f(n) = n · f(n − 1) + f(n − 2)^2 recursive case for n ≥ 2. and g(0, m, r, k) = m base case 0, and g(n, m, r, k) = g(n − 1, r,(k + 2)r + m^2 , k + 1) recursive case for...
Let f and g be two functions whose first and second order derivative functions are continuous,...
Let f and g be two functions whose first and second order derivative functions are continuous, all defined on R. What assumptions on f and g guarantee that the composite function f ◦g is concave?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT