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: 29 feet.
Step-by-step explanation: The formula for the circumference of a circle is C = π d. In order to calculate the diameter of the tree we will use the same formula and solve for d.
91 = 3.14 x d
In order to solve for d you need to divide both sides for 3.14:
D = 28.98, rounded to the nearest foot is 29 feet.
4,9, 36, 49, 121, 144, 196, 225
Y=4^4-100=16-100=-84
Result is -84