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: a: 8.25 b: 49.5
Step-by-step explanation:
Answer:
A ray is a part of a line that has one endpoint and goes on infinitely in only one direction.
Answer:
mean = 4
medin = violet
mode = light blue
range = 4
Step-by-step explanation:
mean = sum/no
mode = largest number
median = (n+1)/2th item
rnge = largest - smllest
The difference is 3ft since the surface area for the prism is 57, and the surface area for the cube is 54.
You can use the surface area formula
2(wl+hl+hw) = Area
2·(3·4.5+2·4.5+2·3)=57
And a cubes surface area formula
6a^2 = Area
6·32=54
