Graph the lines and conic sections r=\frac{1}{(1+2\sin\theta)}

Dottie Parra 2021-08-09 Answered
Graph the lines and conic sections r=1(1+2sinθ)
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Expert Answer

joshyoung05M
Answered 2021-08-10 Author has 97 answers
Step 1
Consider the given polar equation,
r=1(1+2sin(θ))
Compare the given with standard equation of the hyperbola,
r=ke1+2sin(θ)
we get,
e=2 and k=12
so the given equation is the equation of the hyperbola.
Step 2
So, the graph of the hyperbola is,
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I am approximating a solution to a first order LODE using Euler's method. I made two tables, one using a step size of .01 and another using .05 ( I had to start at x=0 and end at x=1). I am not understanding the directions for the second part of my assignment:

It states that the order of numerical methods (like Euler's) is based upon the bound for the cummulative error; i.e. for the cummulative error at, say x=2, is bounded by C h n , where C is a generally unknown constant and n is the order. For Euler's method, plot the points:
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And then fit a line to the above data of the form C h. I don't understand, am I supposed to plot these using a step size of .1 or .05? Or am I supposed to use another step size?
Any clarification is appreciated.
Thanks
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