F(x)=x⁴-1
f'(x)=4x³
Newton’s Method: x[n+1]=x[n]-f(x[n])/f'(x[n]); x[n+1]=x[n]-(x[n]⁴-1)/4x[n]³
x₁=3.00390625
x₂=2.26215...
x₃=1.7182...
X'=X-(X⁴-1)/4X³=X-X/4+1/4X³ is a symbolic way of writing the recursive formula, where X' represents the next iteration.
When X'≈X, -X/4+1/4X³≈0; so X/4≈1/4X³; X≈1/X³, so X⁴≈1 and X⁴-1≈0. But this is f(x)≈0. Hence Newton’s Method converges to a solution.
The rate of change is x[n+1]-x[n]=-(x[n]⁴-1)/4x[n]³=x[n]/4-1/4x[n]³ or symbolically -X/4+1/4X³.
Note that the method converges to one solution. A different x₀ will possibly converge to the solution x=-1.
Answer:
Hello! the answer is A) All Intergers are whole numbers
Step-by-step explanation:
As C) Is not a whole number, and for D) A irrational number cannot be a rational number. B) A Integer can be any whole number it does not have to be a natural number.
Integers
a rational number is any number that can be shown as a fraction or decimal
whole numbers are only positive and the number "0"
integers are numbers that are both positive, negative, and includes "0"
which one do you need help with. (also to find area of Composite Figures break them into smaller shapes and add the areas together)
Should be 2 seconds unless I’m not smart