Infinite Sequences
The sum of the following sequence.
2+4+8+16...
N/A, it is divergent, therefore no possible answer.
Who created Euler's Method?
Leonhard Euler
True or False
Slope fields will represent the slope of a line at each point using mini hashes.
True
When working with a series, it can be one of two types of series.
What are convergent and divergent.
"A list of numbers or objects in a special order" are called...?
What is Euler's method used for?
You can use it to approximate a solution from an initial value through a differentiable equation.
True or False
Slope fields will always look linear.
False
A geometric series will converge only if the common ratio is what number?
r=1
Is this a sequence?
2+4+8+16...
No, this is a series.
What is required for Euler's method?
A box plot to enter values, a differentiable equation, and an initial value.
What does it mean if the hash is parallel with the x-line.
The slope of the line at that point is 0.
P-series will only converge if...
p>1
Truth or False.
The formula for infinite sequences = (An = A1 x r^n-1)
True
True or False
e^i*pi = 0
False, the correct equation is e^i*pi + 1 = 0
True of False
Slope fields can represent lines of functions only, not including ellipses, etc.
False
What series is the following?
Summation = (1/n)^p
P-Series
Carl Friedrich Guass
Yn=Yn-1+hF(Xn-1, Yn-1)
Will the slope at (0,0) always be 0?
No, but in most cases yes.
The following series is a...
5+25+125+625...
Geometric or Arithmic Series